# Jeremy's publications

## 1 Introduction:

This is the list of my publication by inversed chronological order, with various useful informations about it, from the bibtex entries to the structure of the article to help studying their content.

The ACM would like me to add that the documents contained in these directories are included by the contributing authors as a means to ensure timely dissemination of scholarly and technical work on a non-commercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered their works here electronically. It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may not be reposted without the explicit permission of the copyright holder.

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## 2 [IPL2014] "Maximum-weight planar boxes in O(n2) time (and better)"   ISI cJournal ADAPTIVE GEOMETRY tTHEORY

1. Authors
• Jérémy Barbay,
• Timothy M. Chan,
• Gonzalo Navarro,
• Pablo Pérez-Lantero
3. Grant
4. Bibtex
@article{2014-IPL-MaximumWeightPlanarBoxesInON2TimeAndBetter-BarbayChanNavarroPerezLantero,
author    = {J{\'e}r{\'e}my Barbay and
Timothy M. Chan and
Gonzalo Navarro and
Pablo P{\'e}rez-Lantero},
title     = {Maximum-weight planar boxes in $O(n^2)$) time (and better)},
journal   = {Information Processing Letters},
volume    = {114},
number    = {8},
year      = {2014},
pages     = {437-445},
ee        = {http://dx.doi.org/10.1016/j.ipl.2014.03.007},
bibsource = {DBLP, http://dblp.uni-trier.de}
}

5. Highlights
• n points in the plane, each with a positive or negative weight, are considered.
• A maximum box is an axis-aligned rectangle covering the maximum weight sum.
• We find a maximum box in O(n2) time improving upon previous O(n2 log n) algorithms.
• We provide adaptive algorithms improving the complexity on specific instances.
• We show extensions in higher dimensions and the relation with Klee's Measure problem.
6. Keywords

Computational geometry; Maximum box; Divide–summarize-and-conquer; Adaptive algorithms; Klee's Measure problem

7. Abstract

Given a set $$P$$ of $$n$$ points in $${R}^d$$, where each point $$p$$ of $$P$$ is associated with a weight $$w(p)$$ (positive or negative), the Maximum-Weight Box problem is to find an axis-aligned box $$B$$ maximizing $$\sum_{p\in B\cap P}w(p)$$.

We describe algorithms for this problem in two dimensions that run in the worst case in $$O(n^2)$$ time, and much less on more specific classes of instances. In particular, these results imply similar ones for the Maximum Bichromatic Discrepancy Box problem. These improve by a factor of $$\Theta(\lg n)$$ on the previously known worst-case complexity for these problems, $$O(n^2\lg n)$$ [Cortés et al., JALG 2009; Dobkin et al., JCSS 1996]. Although the $$O(n^2)$$ result can be deduced from new results on Klee's Measure problem [Chan, FOCS 2013], it is a more direct and simplified (non-trivial) solution.

We exploit the connection with Klee's Measure problem to further show that

1. the Maximum-Weight Box problem can be solved in $$O(n^d)$$ time for any constant $$d\ge 2$$, improving the mentioned result of $$O(n^{2d-2}\lg n)$$ [Cortés et al., JALG 2009];
2. if the weights are integers bounded by $$O(1)$$ in absolute values, or weights are $$+1$$ and $$-\infty$$ (as in the Maximum Bichromatic Discrepancy Box problem), the Maximum-Weight Box problem can be solved in $$O((n^d/\lg^d n)(\lg\lg n)^{O(1)})$$ time;
3. it is unlikely that the Maximum-Weight Box problem can be solved in less than $$n^{d/2}$$ time (ignoring logarithmic factors) with current knowledge about Klee's Measure problem.
8. Plan
1. Introduction
1. Related work
2. Basic definitions
3. Results
4. Applications to other known problems
5. Higher dimensions and lower bounds
6. Outline
3. $$\delta$$-sensitive analysis
4. Cluster partition analysis
5. Upper and lower bounds in $$d$$ dimensions
1. Connection to \pb{Klee's measure} and higher dimensions
2. Polylogarithmic-factor speedups
3. Problem complexity

## 3 [ALGO2014] "Efficient Fully Compressed Sequence Representations"   ISI cJournal BIGDATA tTHEORY

1. Authors
• Jérémy Barbay, Francisco Claude, Travis Gagie, Gonzalo Navarro, Yakov Nekrich

3. Grants
4. Short Description
• with Francisco Claude, Travis Gagie, Gonzalo Navarro and Yakov Nekrich,
• we introduced the first Compressed Index achieving space within o(n Hk) + O(n) instead of merely within o(n lg σ):
• previous indices were using space within o(n lg σ), which was sometime dominating the n Hk bits used to encoded the compressed data.
5. Bibtex
@article{2014-Algorithmica-EfficientFullyCompressedSequenceRepresentations-BarbayClaudeGagieNavarroNekrich,
author    = {J{\'e}r{\'e}my Barbay and
Francisco Claude and
Travis Gagie and
Gonzalo Navarro and
Yakov Nekrich},
title     = {Efficient Fully-Compressed Sequence Representations},
journal   = {Algorithmica},
volume    = {69},
number    = {1},
year      = {2014},
pages     = {232-268},
ee        = {http://dx.doi.org/10.1007/s00453-012-9726-3},
bibsource = {DBLP, http://dblp.uni-trier.de}
}


## 4 [TCS2013] "On Compressing Permutations and Adaptive Sorting"   ISI cJournal ADAPTIVE BIGDATA tTHEORY

1. Authors
• Jérémy Barbay, Gonzalo Navarro

3. Short Description
• with Gonzalo Navarro,
• we connected formally the concepts of
• compression (of permutations) and
• adaptive algorithms (for sorting) in the comparison model, by
• showing that
• for various adaptive sorting algorithm (in the comparison model),
• there is a compressed data structure for permutations which supports the operators applying this permutation and its inverse in less time than required to decompress the permutation.
4. Grants
5. Bibtex
@article{2013-TCS-CompressedRepresentationsOfPermutationsAndApplications-BarbayNavarro,
author =      {J\'er\'emy Barbay and Gonzalo Navarro},
title =       {On Compressing Permutations and Adaptive Sorting},
journal =      {Theoretical Computer Science ({TCS})},
publisher =   {ELSEVIER},
pages =       {109-123},
volume =      {513},
year =         2013,
annote =      {Keywords: Compression, Permutations, Succinct data structures, Adaptive sorting}
}

6. Citations

Barbay and Navarro \cite{2013-TCS-CompressedRepresentationsOfPermutationsAndApplications-BarbayNavarro} observed that each sorting algorithm in the comparison model yields an encoding for permutations, and that each adaptive sorting algorithm in particular yields a compressed encoding for permutations: this approach inspired several compressed data structures for permutations.

Barbay and Navarro \cite{2013-TCS-CompressedRepresentationsOfPermutationsAndApplications-BarbayNavarro} described various compressed data structures inspired from Wavelet Trees, which use smaller space and support faster the operators on permutations which can be decomposed in a small number of sorted subsequences, either consecutive, non consecutive but always increasing or non consecutive but always monotone.

Barbay and Navarro \cite{2013-TCS-CompressedRepresentationsOfPermutationsAndApplications-BarbayNavarro} observed that each sorting algorithm in the comparison model yields an encoding for permutations, and that each adaptive sorting algorithm in particular yields a compressed encoding for permutations. Focusing on divide and conquer adaptive sorting algorithms such as "Merge Sort", they described various compressed data structures for permutations taking advantage of sorted subsequences in the input.

## 5 [IanFest2013] "From Time to Space: Fast Algorithms That Yield Small and Fast Data Structures"   tTHEORY BIGDATA ADAPTIVE tSURVEY cJournalProject cConference

1. Authors
• Jérémy Barbay
3. Abstract

In many cases, the relation between encoding space and execution time translates into combinatorial lower bounds on the computational complexity of algorithms in the comparison or external memory models. We describe a few cases which illustrate this relation in a distinct direction, where fast algorithms inspire compressed encodings or data structures. In particular, we describe the relation between searching in an ordered array and encoding integers; merging sets and encoding a sequence of symbols; and sorting and compressing permutations.

4. Key words
• Compressed Data Structures
• Permutation
• Set Union
• Sorting
• Unbounded Search
5. Plan
1. Introduction
1. Sorted Search
2. Convex Hull
3. Union of Sorted Sets
4. Sorting
5. Intersection and Threshold Set of Sorted Arrays
6. Pattern Matching in Labeled Trees
3. Encodings and Data Structures
1. Integers
2. Sets and Bit Vectors
3. Ordinal Trees and Planar Graphs
4. Permutations and Functions
5. Strings
6. Binary Relations
7. Labeled Trees and Labeled Planar Graphs
4. Fast Algorithms that yield Compression Schemes
1. From Unbounded Search to Integer Compression
2. From Merging Algorithms to Set and String Compression
3. From Sorting Algorithms to Permutations Data Structures
4. $${\cal H}(vRuns)$$-Adaptive Sorting and Compression:
6. $${\cal H}(vSUS)$$-Adaptive Sorting and Compression:
7. $${\cal H}(vLRM)$$-Adaptive Sorting and Compression:
8. $$nRem$$-Adaptive Sorting and Compression:
9. $$nInv$$-Adaptive Sorting and Compression:
10. Other Adaptive Sorting and Compression:
5. Selected Open Problems
1. From Compression Schemes to Compressed Data Structures:
2. From Compression Schemes to Adaptive Algorithms:
3. Other Compressed Data Structures for Permutations:
4. Sorting and Encoding Multisets:
6. Bibtex
@inproceedings{2013-IanFest-FromTimeToSpace-Barbay,
author    = {J{\'e}r{\'e}my Barbay},
title     = {From Time to Space: Fast Algorithms That Yield Small and
Fast Data Structures},
booktitle = ianfest,
year      = {2013},
pages     = {97-111},
ee        = {http://dx.doi.org/10.1007/978-3-642-40273-9_8},
crossref  = {DBLP:conf/birthday/2013munro},
bibsource = {DBLP, http://dblp.uni-trier.de}
}
@proceedings{DBLP:conf/birthday/2013munro,
editor    = {Andrej Brodnik and
Alejandro L{\'o}pez-Ortiz and
Venkatesh Raman and
Alfredo Viola},
title     = {Space-Efficient Data Structures, Streams, and Algorithms
- Papers in Honor of J. Ian Munro on the Occasion of His
66th Birthday},
booktitle = {Space-Efficient Data Structures, Streams, and Algorithms},
publisher = {Springer},
series    = {Lecture Notes in Computer Science},
volume    = {8066},
year      = {2013},
isbn      = {978-3-642-40272-2},
ee        = {http://dx.doi.org/10.1007/978-3-642-40273-9},
bibsource = {DBLP, http://dblp.uni-trier.de}
}


## 6 [ESA2013] "Theory and Implementation of Online Multiselection Algorithms"   tSIMUL tTHEORY ADAPTIVE cJournalProject cConference

1. Authors
• Jérémy Barbay, Ankur Gupta, Seungbum Jo, Srinivasa Rao, Jonathan Sorenson
3. Grants
4. Bibtex
@inproceedings{2013-ESA-OnlineRankSelect-BarbayGuptaJoRaoSorenson,
author =       {J\'er\'emy Barbay AND Ankur Gupta AND Seungbum Jo AND
S. Srinivasa Rao AND Jonathan Sorenson },
title =        {Theory and Implementation of Online Multiselection Algorithms},
booktitle = esa,
year =         2013,
abstract = {We introduce a new online algorithm for the /multiselection problem/ which performs a sequence of selection queries on a given unsorted array. We show that our online algorithm is 1-competitive in terms of data comparisons. In particular, we match the bounds (up to lower order terms) from the optimal offline algorithm proposed by Kaligosi et al. [ICALP 2005]. We provide experimental results comparing online and offline algorithms. These experiments show that our online algorithms require fewer comparisons than the best-known offline algorithms. Interestingly, our experiments suggest that our optimal online algorithm (when used to sort the array) requires fewer comparisons than both quicksort and mergesort.}

5. Abstract

We introduce a new online algorithm for the multiselection problem which performs a sequence of selection queries on a given unsorted array. We show that our online algorithm is 1-competitive in terms of data comparisons. In particular, we match the bounds (up to lower order terms) from the optimal offline algorithm proposed by Kaligosi et al. [ICALP 2005].

We provide experimental results comparing online and offline algorithms. These experiments show that our online algorithms require fewer comparisons than the best-known offline algorithms. Interestingly, our experiments suggest that our optimal online algorithm (when used to sort the array) requires fewer comparisons than both quicksort and mergesort.

6. Authors
1. Jérémy Barbay
2. Ankur Gupta
3. Seungbum Jo
4. S. Srinivasa Rao
5. Jonathan Sorenson
7. Keywords
• Deferred Data Structure
• Sorting
• Quickselect
• Multiselect
• rank
• select
8. Plan
1. Introduction
1. Motivation.
2. Previous Work.
3. Our Results.
4. Preliminaries.
5. Outline.
2. A Simple Online Algorithm
1. Bitvector.
2. Selection.
3. Terminology
1. Query and Pivot Sets.
2. Pivot Tree and Recursion Depth.
3. Intervals.
4. Gaps.
4. Analysis of the Simple Algorithm
3. Optimal Online Multiselection
1. Algorithm Description
2. Merging
3. Pivot Finding and Partitioning
4. Experimental Results
1. Experimental Setup
2. Results
9. Notes:

The authors discovered later that Motwani and Raghavan \cite{1986-SoCG-DeferredDataStructuringQueryDrivenPreprocessingForGeometricSearchProblems-MotwaniRaghavan} had already explored this topic in 1986, under the distinct name of Deferred Data Structures''. The 1986's resuls are weaker than those of 2013, due to a weaker analysis model, yet the range of applications considered in the 1986's publication is wider and includes data structures for set of planar points supporing queries on the \textsc{convex hulls} in the online model.

## 7 [IC2013] "Compact Binary Relation Representations with Rich Functionality"   ISI tSURVEY cJournal BIGDATA tTHEORY tSIMUL

1. Authors
• Jérémy Barbay, Francisco Claude, Gonzalo Navarro
3. Grants
4. Short Description
• with Francisco Claude and Gonzalo Navarro,
• we unified the various Compressed Data Structures for Binary Relations previously known
• into a single common theoretical interface, and explored in practice various implementation alternatives.
5. Bibtex
@article{2013-IC-CompactBinaryRelationRepresentationsWithRichFunctionality-BarbayClaudeNavarro,
AUTHOR = "J. Barbay and F. Claude and G. Navarro",
TITLE = "Compact Binary Relation Representations with Rich Functionality",
JOURNAL = "Information and Computation",
PUBLISHER = "Elsevier",
YEAR = 2013,
VOLUME = 232,
PAGES = "19--37"
}


## 8 [CCCG2013] "Maximum-Weight Planar Boxes in O(n2) Time (and Better)"   tTHEORY ADAPTIVE GEOMETRY cConference

1. Authors
• Jérémy Barbay, Timothy M. Chan, Gonzalo Navarro, Pablo Pérez-Lantero
3. Grants
4. Bibtex
@inproceedings{2013-CCCG-MaximumWeightPlanarBoxesInON2TimeAndBetter-BarbayChanNavarroPerezLantero,
author    = {J{\'e}r{\'e}my Barbay and
Timothy M. Chan and
Gonzalo Navarro and
Pablo P{\'e}rez-Lantero},
title     = {Maximum-Weight Planar Boxes in O(n$^{\mbox{2}}$) Time (and
Better)},
booktitle = {CCCG},
year      = {2013},
ee        = {http://cccg.ca/proceedings/2013/papers/paper_3.pdf},
crossref  = {DBLP:conf/cccg/2013},
bibsource = {DBLP, http://dblp.uni-trier.de}
}

@proceedings{DBLP:conf/cccg/2013,
title     = {Proceedings of the 25th Canadian Conference on Computational
Geometry, CCCG 2013, Waterloo, Ontario, Canada, August 8-10,
2013},
booktitle = {CCCG},
publisher = {Carleton University, Ottawa, Canada},
year      = {2013},
ee        = {http://cccg.ca/proceedings/2013/},
bibsource = {DBLP, http://dblp.uni-trier.de}
}

5. Keywords

Computational geometry; Maximum box; Divide–summarize-and-conquer; Adaptive algorithms; Klee's Measure problem

6. Abstract

Given a set $$P$$ of $$n$$ points in $${R}^d$$, where each point $$p$$ of $$P$$ is associated with a weight $$w(p)$$ (positive or negative), the Maximum-Weight Box problem is to find an axis-aligned box $$B$$ maximizing $$\sum_{p\in B\cap P}w(p)$$.

We describe algorithms for this problem in two dimensions that run in the worst case in $$O(n^2)$$ time, and much less on more specific classes of instances. In particular, these results imply similar ones for the Maximum Bichromatic Discrepancy Box problem. These improve by a factor of $$\Theta(\lg n)$$ on the previously known worst-case complexity for these problems, $$O(n^2\lg n)$$ [Cortés et al., JALG 2009; Dobkin et al., JCSS 1996]. Although the $$O(n^2)$$ result can be deduced from new results on Klee's Measure problem [Chan, FOCS 2013], it is a more direct and simplified (non-trivial) solution.

We exploit the connection with Klee's Measure problem to further show that

1. the Maximum-Weight Box problem can be solved in $$O(n^d)$$ time for any constant $$d\ge 2$$, improving the mentioned result of $$O(n^{2d-2}\lg n)$$ [Cortés et al., JALG 2009];
2. if the weights are integers bounded by $$O(1)$$ in absolute values, or weights are $$+1$$ and $$-\infty$$ (as in the Maximum Bichromatic Discrepancy Box problem), the Maximum-Weight Box problem can be solved in $$O((n^d/\lg^d n)(\lg\lg n)^{O(1)})$$ time;
3. it is unlikely that the Maximum-Weight Box problem can be solved in less than $$n^{d/2}$$ time (ignoring logarithmic factors) with current knowledge about Klee's Measure problem.
7. Plan
1. Introduction
1. Related work
2. Basic definitions
3. Results
4. Applications to other known problems
5. Outline
3. $$\delta$$-sensitive analysis
4. Cluster partition analysis
5. Discussion
1. Connection to Klee's measure problem and higher dimensions
2. Polylogarithmic-factor speedups and applications
6. Perspectives
1. Potential Lower bounds
2. Generalization to higher dimensions

## 9 [BitsDeCiencias2013] "Chocolate Mousse y Algoritmos"   PEDAGOGY cPopular

1. Authors
• Jérémy Barbay

## 10 [ALGO2012] "Succinct Representation of Labeled Graphs"   ISI cJournal BIGDATA tTHEORY

1. Authors
• Jérémy Barbay, Castelli, Aleardi, He, Ian J. Munro
3. Grants
4. Bibtex
@article{2012-Algoritmica-SuccinctRepresentationOfLabeledGraphs-BarbayCastelliAleardiHeMunro,
author =       {J\'er\'emy Barbay and Luca Castelli Aleardi and Meng He and J. Ian Munro},
title =        {Succinct Representation of Labeled Graphs},
journal =      {Algorithmica},
pages =        {224-257},
volume =       {62(1-2)},
year      = 2012,
abstract = {In many applications, properties of an object being
modeled are stored as labels on vertices or edges of a graph. In this
paper, we consider succinct representation of labeled graphs. Our main
results are the succinct representations of labeled and multi-labeled
graphs (we consider vertex labeled planar triangulations, as well as
edge labeled planar graphs and the more general k-book embedded
graphs) to support various label queries efficiently. The additional
space cost to store the labels is essentially the
information-theoretic minimum. As far as we know, our representations
are the first succinct representations of labeled graphs. We also have
two preliminary results to achieve the main results. First, we design
a succinct representation of unlabeled planar triangulations to
support the rank/select of edges in ccw (counter clockwise) order in
addition to the other operations supported in previous work. Second,
we design a succinct representation for a k-book embedded graph when k
is large to support various navigational operations more
efficiently. In particular, we can test the adjacency of two vertices
in O(lg(k)lg(lg(k))) time, while previous work uses O(k) time.}
}


## 11 [TCS2012] "LRM-Trees Compressed Indices Adaptive Sorting and Compressed Permutations"   ISI cJournal ADAPTIVE BIGDATA tTHEORY

1. Authors
• Jérémy Barbay, Johannes Fischer, Gonzalo Navarro
3. Grants
4. Abstract:

LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to index integer arrays in order to support range minimum queries on them. We describe how they yield many other convenient results in a variety of areas: compressed succinct indices for range minimum queries on partially sorted arrays; a new adaptive sorting algorithm; and a compressed succinct data structure for permutations supporting direct and inverse application in time inversely proportional to the permutation's compressibility.

5. Authors:
6. Bibtex
@article{2012-TCS-LRMTreesCompressedIndicesAdaptiveSortingAndCompressedPermutations-BarbayFischerNavarro,
author    = {J{\'e}r{\'e}my Barbay and
Johannes Fischer and
Gonzalo Navarro},
title     = {{LRM}-Trees: Compressed indices, adaptive sorting, and compressed
permutations},
journal   = {{ELSEVIER} Theoretical Computer Science ({TCS})},
volume    = 459,
year      = 2012,
pages     = {26-41},
ee        = {http://dx.doi.org/10.1016/j.tcs.2012.08.010},
bibsource = {DBLP, http://dblp.uni-trier.de}
}


## 12 [CCCG2012] "Adaptive Techniques to Find Optimal Planar Boxes"   tTHEORY GEOMETRY ADAPTIVE cConference

1. Description for Humans

Adaptive Techniques to find Optimal Planar Boxes, Jeremy Barbay, Gonzalo Navarro and Pablo Perez-Lantero, Annual Canadian Conference on Computational Geometry (CCCG) 2012

2. Authors
• Jérémy Barbay, Gonzalo Navarro, Pablo Perez-Lantero
4. Grants
5. Bibtex
@inproceedings{2012-CCCG-AdaptiveTechniquesToFindOptimalPlanarBoxes-BarbayNavarroPerezLantero,
author    = {J{\'e}r{\'e}my Barbay and
Gonzalo Navarro and
Pablo P{\'e}rez-Lantero},
title     = {Adaptive Techniques to find Optimal Planar Boxes},
booktitle = {CCCG},
year      = {2012},
pages     = {71-76},
ee        = {http://2012.cccg.ca/papers/paper2.pdf},
crossref  = {DBLP:conf/cccg/2012},
bibsource = {DBLP, http://dblp.uni-trier.de}
}
@proceedings{DBLP:conf/cccg/2012,
title     = {Proceedings of the 24th Canadian Conference on Computational
Geometry, CCCG 2012, Charlottetown, Prince Edward Island,
booktitle = {CCCG},
year      = 2012,
ee        = {http://2012.cccg.ca/papers.html},
bibsource = {DBLP, http://dblp.uni-trier.de}
}


## 13 [SIGACT2012] "Review of understanding and applying cryptography and data security by Adam J. Elbirt."   CRYPTO cJournal

1. Authors
• Jérémy Barbay
2. Bibtex
@article{2012-SIGACT-ReviewOfUnderstandingAndApplyingCryptographyAndDataSecurity-Barbay,
author    = {J{\'e}r{\'e}my Barbay},
title     = {Review of understanding and applying cryptography and data
journal   = {SIGACT News},
volume    = {43},
number    = {1},
year      = {2012},
pages     = {18-21},
ee        = {http://doi.acm.org/10.1145/2160649.2160655},
bibsource = {DBLP, http://dblp.uni-trier.de}
}


## 14 [TALG2011] "Succinct indexes for strings, binary relations and multilabeled trees"   ISI cJournal BIGDATA tTHEORY

1. Authors
• Jérémy Barbay, Meng He, J. Ian Munro, Srinivasa Rao Satti

3. Short Description
• with Meng He, Ian J. Munro, and Srinivasa Rao,
• we introduced formally the concept of Succinct Indexes:
• some succinct data structures previously introduced were indexes without claiming it, nor the advantages of indexes such as
• their modularity (two succinct indexes supporting distinct operators can be combined into a single succinct index which supports the union of their operator sets, which is not necessarily true of two succinct data structures) or
• their applications to generate compressed data structures.
4. Grants
5. Bibtex
@article{2011-TALG-SuccinctIndexesForStringsBinaryRelationsAndMultiLabeledTrees-BarbayHeMundroSatti,
author    = {J{\'e}r{\'e}my Barbay and
Meng He and
J. Ian Munro and
Srinivasa Rao Satti},
title     = {Succinct indexes for strings, binary relations and multilabeled
trees},
journal   = {ACM Transactions on Algorithms},
volume    = {7},
number    = {4},
year      = {2011},
pages     = {52},
ee        = {http://doi.acm.org/10.1145/2000807.2000820},
bibsource = {DBLP, http://dblp.uni-trier.de}
}


## 15 [CPM2011] "LRM-Trees: Compressed Indices, Adaptive Sorting, and Compressed Permutations"   tTHEORY ADAPTIVE BIGDATA cConference

1. Authors
• Jérémy Barbay, Johannes Fischer, Gonzalo Navarro
3. Grants
4. Abstract:

LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to index integer arrays in order to support range minimum queries on them. We describe how they yield many other convenient results in a variety of areas: compressed succinct indices for range minimum queries on partially sorted arrays; a new adaptive sorting algorithm; and a compressed succinct data structure for permutations supporting direct and inverse application in time inversely proportional to the permutation's compressibility.

5. Authors:
6. Bibtex
@inproceedings{2011-CPM-LRMTrees-BarbayFischerNavarro,
author    = {J{\'e}r{\'e}my Barbay and
Johannes Fischer and
Gonzalo Navarro},
title     = {{LRM}-Trees: Compressed Indices, Adaptive Sorting, and Compressed
Permutations},
booktitle = cpm,
year      = {2011},
pages     = {285-298},
ee        = {http://dx.doi.org/10.1007/978-3-642-21458-5_25},
crossref  = {DBLP:conf/cpm/2011},
bibsource = {DBLP, http://dblp.uni-trier.de}
}

@proceedings{DBLP:conf/cpm/2011,
editor    = {Raffaele Giancarlo and
Giovanni Manzini},
title     = {Combinatorial Pattern Matching - 22nd Annual Symposium,
CPM 2011, Palermo, Italy, June 27-29, 2011. Proceedings},
booktitle = {CPM},
publisher = {Springer},
series    = {Lecture Notes in Computer Science},
volume    = {6661},
year      = {2011},
isbn      = {978-3-642-21457-8},
ee        = {http://dx.doi.org/10.1007/978-3-642-21458-5},
bibsource = {DBLP, http://dblp.uni-trier.de}
}


## 16 [Chapter2010] "Randomized Complexity"   PEDAGOGY cChapter

1. Authors
• Jérémy Barbay
3. Bibtex
  @InBook{2010-Chapter-RandomizedComplexity-Barbay,
author =       {J{\'e}r{\'e}my Barbay},
title =        {Randomized Complexity},
chapter =      {2},
publisher =    {Wiley},
year =         2010,
volume =       1,
month =        {August},
pages =        {21-38},
note =         {ISBN: 978-1-84821-147-6}
}
@book{2010-Book-ConceptsofCombinatorialOptimzation-Paschos,
title={Concepts of Combinatorial Optimization},
author={Vangelis Th Paschos},
isbn={9781848211476},
lccn={2010018423},
series={Combinatorial Optimization},
year={2010},
publisher={Wiley}
}


## 17 [ISAAC2010] "Alphabet Partitioning for Compressed Rank Select and Applications"   tTHEORY BIGDATA cConference

1. Authors
• Jérémy Barbay, Travis Gagie, Gonzalo Navarro, Yakov Nekrich
3. Bibtex
@inproceedings{2010-ISAAC-AlphabetPartitioningForCompressedRankSelectAndApplications-BarbayGagieNavarroNekrich,
author    = {J{\'e}r{\'e}my Barbay and
Travis Gagie and
Gonzalo Navarro and
Yakov Nekrich},
title     = {Alphabet Partitioning for Compressed Rank/Select and Applications},
booktitle = isaac,
year      = {2010},
pages     = {315-326},
ee        = {http://dx.doi.org/10.1007/978-3-642-17514-5_27},
crossref  = {DBLP:conf/isaac/2010-2},
bibsource = {DBLP, http://dblp.uni-trier.de}
}
@proceedings{DBLP:conf/isaac/2010-2,
editor    = {Otfried Cheong and
Kyung-Yong Chwa and
Kunsoo Park},
title     = {Algorithms and Computation - 21st International Symposium,
ISAAC 2010, Jeju Island, Korea, December 15-17, 2010, Proceedings,
Part II},
booktitle = {ISAAC (2)},
publisher = {Springer},
series    = {Lecture Notes in Computer Science (LNCS)},
volume    = {6507},
year      = {2010},
isbn      = {978-3-642-17513-8},
ee        = {http://dx.doi.org/10.1007/978-3-642-17514-5},
bibsource = {DBLP, http://dblp.uni-trier.de}
}


## 18 [LATIN2010] "Compact Rich-Functional Binary Relation Representations"   tTHEORY BIGDATA cConference

1. Authors
• Jérémy Barbay, Francisco Claude, Gonzalo Navarro
3. Bibtex
@inproceedings{2010-LATIN-CompactRichFunctionalBinaryRelationRepresentations-BarbayClaudeNavarro,
author    = {J{\'e}r{\'e}my Barbay and
Francisco Claude and
Gonzalo Navarro},
title     = {Compact Rich-Functional Binary Relation Representations},
booktitle = latin,
year      = {2010},
pages     = {170-183},
ee        = {http://dx.doi.org/10.1007/978-3-642-12200-2_17},
crossref  = {DBLP:conf/latin/2010},
bibsource = {DBLP, http://dblp.uni-trier.de}
}

@proceedings{DBLP:conf/latin/2010,
editor    = {Alejandro L{\'o}pez-Ortiz},
title     = {LATIN 2010: Theoretical Informatics, 9th Latin American
Symposium, Oaxaca, Mexico, April 19-23, 2010. Proceedings},
publisher = {Springer},
series    = {Lecture Notes in Computer Science},
volume    = {6034},
year      = {2010},
isbn      = {978-3-642-12199-9},
ee        = {http://dx.doi.org/10.1007/978-3-642-12200-2},
bibsource = {DBLP, http://dblp.uni-trier.de}
}


## 19 [JEA2009] "An Experimental Investigation of Set Intersection Algorithms for Text Searching"   tSIMUL ADAPTIVE cJournal

1. Authors
• Jérémy Barbay, Lopez, Ortiz, Lu, Salinger
3. Bibtex
@article{2009-JEA-AnExperimentalInvestigationOfSetIntersectionAlgorithmsForTextSearching-BarbayLopezOrtizLuSalinger,
author    = {J{\'e}r{\'e}my Barbay and
Alejandro L{\'o}pez-Ortiz and
Tyler Lu and
Alejandro Salinger},
title     = {An experimental investigation of set intersection algorithms
for text searching},
journal   = jea,
volume    = {14},
year      = {2009},
ee        = {http://doi.acm.org/10.1145/1498698.1564507},
bibsource = {DBLP, http://dblp.uni-trier.de}
}


## 20 [STACS2009] "Compressed Representations of Permutations and Applications"   tTHEORY ADAPTIVE BIGDATA cConference

1. Authors
• Jérémy Barbay, Gonzalo Navarro
3. Bibtex
@inproceedings{2009-STACS-CompressedRepresentationsOfPermutationsAndApplications-BarbayNavarro,
author    = {J{\'e}r{\'e}my Barbay and
Gonzalo Navarro},
title     = {Compressed Representations of Permutations, and Applications},
booktitle = stacs,
year      = {2009},
pages     = {111-122},
ee        = {http://dx.doi.org/10.4230/LIPIcs.STACS.2009.1814},
crossref  = {DBLP:conf/stacs/2009},
bibsource = {DBLP, http://dblp.uni-trier.de}
}

@proceedings{DBLP:conf/stacs/2009,
editor    = {Susanne Albers and
Jean-Yves Marion},
title     = {26th International Symposium on Theoretical Aspects of Computer
Science, STACS 2009, February 26-28, 2009, Freiburg, Germany,
Proceedings},
booktitle = {STACS},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
series    = {LIPIcs},
volume    = {3},
year      = {2009},
isbn      = {978-3-939897-09-5},
ee        = {http://stacs2009.informatik.uni-freiburg.de/proceedings.php},
bibsource = {DBLP, http://dblp.uni-trier.de}
}


## 21 [SCCC2009] "Adaptive Algorithm for Threshold Path Subset Queries"   tTHEORY ADAPTIVE cConference

1. Authors
3. Bibtex
@inproceedings{2009-SCCC-AdaptiveAlgorithmsForThresholdPathSubsetQueries-BarbayVeraskouski,
author    = {J{\'e}r{\'e}my Barbay and
title     = {Adaptive Algorithm for Threshold Path Subset Queries},
booktitle = sccc,
year      = {2009},
pages     = {3-10},
ee        = {http://doi.ieeecomputersociety.org/10.1109/SCCC.2009.17},
crossref  = {DBLP:conf/sccc/2009},
bibsource = {DBLP, http://dblp.uni-trier.de}
}

@proceedings{DBLP:conf/sccc/2009,
editor    = {Marcelo Arenas and
Benjamin Bustos},
title     = {2009 International Conference of the Chilean Computer Science
Society, SCCC 2009, Santiago, Chile, November 10-12, 2009},
booktitle = {SCCC},
publisher = {IEEE Computer Society},
year      = {2009},
isbn      = {978-0-7695-4137-2},
bibsource = {DBLP, http://dblp.uni-trier.de}
}


## 22 [SCCC2009] "Efficient Algorithms for Context Query Evaluation over a Tagged Corpus"   tTHEORY ADAPTIVE cConference

1. Authors
• Jérémy Barbay, Alex L
3. Bibtex
@inproceedings{2009-SCCC-EfficientAlgorithmsForContextQueryEvaluationOverATaggedCorpus-BarbayLopezOrtiz,
author    = {J{\'e}r{\'e}my Barbay and
Alex L{\'o}pez-Ortiz},
title     = {Efficient Algorithms for Context Query Evaluation over a
Tagged Corpus},
booktitle = sccc,
year      = {2009},
pages     = {11-17},
ee        = {http://doi.ieeecomputersociety.org/10.1109/SCCC.2009.16},
crossref  = {DBLP:conf/sccc/2009},
bibsource = {DBLP, http://dblp.uni-trier.de}
}


## 23 [FOCS2009] "Instance-Optimal Geometric Algorithms"   tTHEORY ADAPTIVE GEOMETRY cJournalProject cConference

1. Authors
• Peyman Afshani, Jérémy Barbay, Timothy M. Chan

3. Short Description
• with Peyman Afshani and Timothy Chan,
• we gave the first applications of (input order oblivious) Instance Optimality to Computational Geometry, a fundamental result which generalize to many other problems in computational geometry.
• (The concept of Instance Optimality had been previously introduced by Fagin et al. on queries to databases.)
4. Abstract

We prove the existence of an algorithm A for computing 2-d or 3-d convex hulls that is optimal for every point set in the following sense: for every set S of n points and for every algorithm A' in a certain class C, the maximum running time of A on input s1,…,sn is at most a constant factor times the maximum running time of A' on s1,…,sn, where the maximum is taken over all permutations s1,…,sn of S.

In fact, we can establish a stronger property: for every S and A', the maximum running time of A is at most a constant factor times the average running time of A' over all permutations of S. We call algorithms satisfying these properties instance-optimal in the order-oblivious and random-order setting. Such instance-optimal algorithms simultaneously subsume output-sensitive algorithms and distribution-dependent average-case algorithms, and all algorithms that do not take advantage of the order of the input or that assume the input is given in a random order. The class C under consideration consists of all algorithms in a decision tree model where the tests involve only multilinear functions with a constant number of arguments.

To establish an instance-specific lower bound, we deviate from traditional Ben-Or-style proofs and adopt an interesting adversary argument. For 2-d convex hulls, we prove that a version of the well known algorithm by Kirkpatrick and Seidel (1986) or Chan, Snoeyink, and Yap (1995) already attains this lower bound. For 3-d convex hulls, we propose a new algorithm.

To demonstrate the potential of the concept, we further obtain instance-optimal results for a few other standard problems in computational geometry, such as maxima in 2-d and 3-d, orthogonal line segment intersection in 2-d, finding bichromatic L-close pairs in 2-d, off-line orthogonal range searching in 2-d, off-line dominance reporting in 2-d and 3-d, off-line halfspace range reporting in 2-d and 3-d, and off-line point location in 2-d.

5. Bibtex
@inproceedings{2009-FOCS-InstanceOptimalGeometricAlgorithms-AfshaniBarbayChan,
author    = {Peyman Afshani and
J{\'e}r{\'e}my Barbay and
Timothy M. Chan},
title     = {Instance-Optimal Geometric Algorithms},
booktitle = focs,
year      = {2009},
pages     = {129-138},
ee        = {http://doi.ieeecomputersociety.org/10.1109/FOCS.2009.34},
crossref  = {DBLP:conf/focs/2009},
bibsource = {DBLP, http://dblp.uni-trier.de},
abstract =  {We prove the existence of an algorithm A for computing
2-d or 3-d convex hulls that is optimal for every
point set in the following sense: for every set S of
n points and for every algorithm A' in a certain
class C, the maximum running time of A on input
s_1,...,s_n is at most a constant factor times the
maximum running time of A' on s_1,...,s_n, where the
maximum is taken over all permutations s_1,...,s_n
of S. In fact, we can establish a stronger property:
for every S and A', the maximum running time of A is
at most a constant factor times the average running
time of A' over all permutations of S. We call
algorithms satisfying these properties
instance-optimal in the order-oblivious and
random-order setting. Such instance-optimal
algorithms simultaneously subsume output-sensitive
algorithms and distribution-dependent average-case
algorithms, and all algorithms that do not take
advantage of the order of the input or that assume
the input is given in a random order.  The class C
under consideration consists of all algorithms in a
decision tree model where the tests involve only
multilinear functions with a constant number of
arguments. To establish an instance-specific lower
bound, we deviate from traditional Ben-Or-style
argument. For 2-d convex hulls, we prove that a
version of the well known algorithm by Kirkpatrick
and Seidel (1986) or Chan, Snoeyink, and Yap (1995)
already attains this lower bound. For 3-d convex
hulls, we propose a new algorithm.  To demonstrate
the potential of the concept, we further obtain
instance-optimal results for a few other standard
problems in computational geometry, such as maxima
in 2-d and 3-d, orthogonal line segment intersection
in 2-d, finding bichromatic L_\infty-close pairs in
2-d, off-line orthogonal range searching in 2-d,
off-line dominance reporting in 2-d and 3-d,
off-line halfspace range reporting in 2-d and 3-d,
and off-line point location in 2-d.  }
}

@proceedings{DBLP:conf/focs/2009,
title     = {50th Annual IEEE Symposium on Foundations of Computer Science,
FOCS 2009, October 25-27, 2009, Atlanta, Georgia, USA},
booktitle = {FOCS},
publisher = {IEEE Computer Society},
year      = {2009},
isbn      = {978-0-7695-3850-1},
bibsource = {DBLP, http://dblp.uni-trier.de}
}


In collaboration with Peyman Afshani and Timothy Chan, we proved the existence of an algorithm $$A$$ for computing 2-d or 3-d convex hulls that is optimal for every point set in the following sense: for every sequence $$S$$ of $$n$$ points and for every algorithm $$A'$$ in a certain class $$A$$, the maximum running time of $$A$$ on input $$S$$ is at most a constant factor times the running time of $$A'$$ on the worst possible permutation of $$S$$ for $$A'$$. In fact, we can establish a stronger property: for every sequence $$S$$ of points and every algorithm $$A'$$, the maximum running time of algorithm $$A$$ is at most a constant factor times the average running time of $$A'$$ over all permutations of $$S$$. We call algorithms satisfying these properties instance-optimal in the order-oblivious and random-order setting. Such instance-optimal algorithms simultaneously subsume output-sensitive algorithms and distribution-dependent average-case algorithms, and all algorithms that do not take advantage of the order of the input or that assume the input is given in a random order.

The class $$A$$ under consideration consists of all algorithms in a decision tree model where the tests involve only multilinear functions with a constant number of arguments. To establish an instance-specific lower bound, we deviate from traditional Ben–Or-style proofs and adopt an interesting adversary argument. For 2-d convex hulls, we prove that a version of the well known algorithm by Kirkpatrick and Seidel (1986) or Chan, Snoeyink, and Yap (1995) already attains this lower bound. For 3-d convex hulls, we propose a new algorithm.

We further obtain instance-optimal results for a few other standard problems in computational geometry, such as maxima in 2-d and 3-d, orthogonal line segment intersection in 2-d, finding bichromatic $$L_\infty$$-close pairs in 2-d, off-line orthogonal range searching in 2-d, off-line dominance reporting in 2-d and 3-d, off-line halfspace range reporting in 2-d and 3-d, and off-line point location in 2-d.

## 24 [TALG2008] "Alternation and Redundancy Analysis of the Intersection Problem"   tTHEORY ADAPTIVE cJournal

1. Authors
• Jérémy Barbay, Claire Kenyon-Mathieu
3. Bibtex
@article{2008-TALG-AlternationAndRedundancyAnalysisOfTheIntersectionProblem-BarbayKenyon,
author = {Barbay, J{\'e}r{\'e}my and Kenyon, Claire},
title = {Alternation and redundancy analysis of the intersection problem},
issue_date = {March 2008},
volume = {4},
number = {1},
month = mar,
year = {2008},
issn = {1549-6325},
pages = {4:1--4:18},
articleno = {4},
numpages = {18},
url = {http://doi.acm.org/10.1145/1328911.1328915},
doi = {10.1145/1328911.1328915},
acmid = {1328915},
publisher = {ACM},
address = {New York, NY, USA},
keywords = {Adaptive analysis, alternation analysis, intersection, intersection of sorted arrays, randomized algorithm, redundancy analysis},
journal =      {ACM Transactions on Algorithms ({TALG})},
keywords = {randomized algorithm, intersection of sorted arrays, alternation and redundancy adaptive analysis},
abstract = {The intersection of sorted arrays problem has applications in search engines such as Google.
Previous work propose and compare deterministic algorithms for this problem, in an adaptive
analysis based on the encoding size of a certificate of the result (cost analysis). We define the
alternation analysis, based on the non-deterministic complexity of an instance. In this analysis we
prove that there is a deterministic algorithm asymptotically performing as well as any randomized
algorithm in the comparison model. We define the redundancy analysis, based on a measure of
the internal redundancy of the instance. In this analysis we prove that any algorithm optimal
in the redundancy analysis is optimal in the alternation analysis, but that there is a randomized
algorithm which performs strictly better than any deterministic algorithm in the comparison
model. Finally, we describe how those results can be extended beyond the comparison model.
}
}


## 25 [CCCG2008] "Convex Hull of the Union of Convex Objects in the Plane"   tTHEORY GEOMETRY ADAPTIVE cJournalProject cConference

1. Authors
• Jérémy Barbay, Eric Y. Chen
3. Bibtex
@inproceedings{2008-CCCG-ConvexHullOfTheUnionOfConvexObjectsInThePlane-BarbayChen,
author    = {J{\'e}r{\'e}my Barbay and
Eric Y. Chen},
title     = {Convex Hull of the Union of Convex Objects in the Plane:
booktitle = cccg,
year      = {2008},
crossref  = {DBLP:conf/cccg/2008},
bibsource = {DBLP, http://dblp.uni-trier.de}
}
@proceedings{DBLP:conf/cccg/2008,
title     = {Proceedings of the 20th Annual Canadian Conference on Computational
Geometry, Montr{\'e}al, Canada, August 13-15, 2008},
booktitle = {CCCG},
year      = {2008},
bibsource = {DBLP, http://dblp.uni-trier.de}
}

4. Abstract

An adaptive algorithm is one which performance can be expressed more precisely than as a mere function of the size of the input: output-sensitive algorithms are a special case of adaptive algorithms. We consider the computation of the convex hull of a set of convex hulls, for instance in the case where the set of points has been composed from simpler objects from a library, for each of which the convex hull has been precomputed. We show that in this context an adaptive algorithm performs better if it takes advantage of other features than the size of the output.

## 26 [EoA2008] "Succinct Encoding of Permutations: Applications to Text Indexing"   BIGDATA tSURVEY cChapter

1. Authors
• Jérémy Barbay, J. Ian Munro
3. Erratas:
• Page 3, line 18, "(e.g. $$f^5(9)=f^3(9)=3$$)" should be replaced by "(e.g. $$f^5(9)=f^2(3)=3$$)"
4. Bibtex
@incollection{2008-EoA-SuccinctEncodingOfPermutationsApplicationsToTextIndexing-BarbayMunro,
author    = {J{\'e}r{\'e}my Barbay and
J. Ian Munro},
title     = {Succinct Encoding of Permutations: Applications to Text Indexing},
booktitle = eoa,
pages     = {915-919},
year      = {2008},
ee        = {http://dx.doi.org/10.1007/978-0-387-30162-4_411},
crossref  = {DBLP:reference/algo/2008},
bibsource = {DBLP, http://dblp.uni-trier.de}
}

@book{DBLP:reference/algo/2008,
editor    = {Ming-Yang Kao},
title     = {Encyclopedia of Algorithms},
publisher = {Springer},
year      = {2008},
isbn      = {978-0-387-30162-4},
bibsource = {DBLP, http://dblp.uni-trier.de}
}

5. Title

Succinct Encoding of Permutations and its Applications to Text Indexing (2003; Munro, Raman, Raman, Rao)

6. Authors

Jérémy Barbay (University of Waterloo), J. Ian Munro (University of Waterloo).

7. Index Terms

Succinct Data Structures, Permutations, Functions, Text Strings, Binary Relations

8. Plan
1. PROBLEM DEFINITION
2. KEY RESULTS
3. APPLICATIONS
1. Functions
2. Text Strings
3. Binary Relations
4. OPEN PROBLEMS
5. EXPERIMENTAL RESULTS
6. DATA SETS
7. URL to CODE
8. CROSS REFERENCES

## 27 [TCS2007] "Adaptive Searching in Succinctly Encoded Binary Relations and Tree Structured Documents"   ISI cJournal ADAPTIVE BIGDATA tTHEORY

1. Authors
• Jérémy Barbay, Alexander Golynski, Ian J. Munro, Srinivasa Rao
3. Bibtex
@article{2007-TCS-AdaptiveSearchingInSuccinctlyEncodedBinaryRelationsAndTreeStructuredDocuments-BarbayGolynskiMunroRao,
author =       {J{\'e}r{\'e}my Barbay and Alexander Golynski and J. Ian Munro and S. Srinivasa Rao},
title =        {Adaptive Searching in Succinctly Encoded Binary Relations and Tree-Structured Documents},
journal =      {{ELSEVIER} Theoretical Computer Science ({TCS})},
year =         2007,
key =          {TCS6592},
month =        {October},
abstract = {
The methods most heavily used by search engines to answer
conjunctive queries on binary relations (such as one associating
keywords with web pages) are based on computing the intersection of
postings lists stored as sorted arrays and using variants of binary
search.  We show that a succinct representation of the binary
relation permits much better results, while using less space than
traditional methods. We apply our results not only to conjunctive
queries on binary relations, but also to queries on semi-structured
documents such as XML documents or file-system indexes, using a
variant of an adaptive algorithm used to solve conjunctive queries
on binary relations.
}
}


## 28 [ISAAC2007] "Succinct Representation of Labeled Graphs"   tTHEORY BIGDATA cConference

1. Authors
• Jérémy Barbay, Luca Castelli-Aleardi, Meng He, Ian J. Munro
3. Grants
4. Bibtex
@inproceedings{2007-ISAAC-SuccinctRepresentationOfLabeledGraphs-BarbayCastelliAleardiHeMunro,
author =       {J\'er\'emy Barbay and Luca Castelli Aleardi and Meng He and J. Ian Munro},
title =        {Succinct Representation of Labeled Graphs},
booktitle = isaac,
pages =        {575-584},
publisher = {Springer},
series    = {Lecture Notes in Computer Science ({LNCS})},
volume =       2906,
year      = 2007,
abstract = {In many applications, properties of an object being
modeled are stored as labels on vertices or edges of a graph. In this
paper, we consider succinct representation of labeled graphs. Our main
results are the succinct representations of labeled and multi-labeled
graphs (we consider vertex labeled planar triangulations, as well as
edge labeled planar graphs and the more general k-book embedded
graphs) to support various label queries efficiently. The additional
space cost to store the labels is essentially the
information-theoretic minimum. As far as we know, our representations
are the first succinct representations of labeled graphs. We also have
two preliminary results to achieve the main results. First, we design
a succinct representation of unlabeled planar triangulations to
support the rank/select of edges in ccw (counter clockwise) order in
addition to the other operations supported in previous work. Second,
we design a succinct representation for a k-book embedded graph when k
is large to support various navigational operations more
efficiently. In particular, we can test the adjacency of two vertices
in O(lg(k)lg(lg(k))) time, while previous work uses O(k) time.}
}


## 29 [SODA2007] "Succinct Indexes for Strings Binary Relations and Multi Labeled Trees"   tTHEORY BIGDATA cConference

1. Authors
• Jérémy Barbay, Meng He, Ian J. Munro, Srinivasa Rao
3. Bibtex
@inproceedings{2007-SODA-SuccinctIndexesForStringsBinaryRelationsAndMultiLabeledTrees-BarbayHeMunroRao,
author =       {J{\'e}r{\'e}my Barbay and Meng He and J. Ian Munro and S. Srinivasa Rao},
title =        {Succinct Indexes for Strings, Binary Relations and Multi-Labeled Trees},
booktitle =    soda,
pages =        {680--689},
DISABLEDorganization = {ACM-SIAM},
publisher = {ACM},
year =         {2007},
postscript =   {http://www.cs.uwaterloo.ca/~jbarbay/Recherche/Publishing/Publications/sisabr_soda.ps},
pdf = {http://www.cs.uwaterloo.ca/~jbarbay/Recherche/Publishing/Publications/sisabr_soda.pdf},
abstract = {We define and design succinct indexes for several
abstract data types (ADTs).  The concept is to design auxiliary data
structures called succinct indexes that occupy asymptotically less
space than the information-theoretic lower bound on the space required
to encode the given data, and support an extended set of operations
using the basic operators defined in the ADT.  As opposed to succinct
encodings, The main advantage of succinct indexes is that we make
assumptions only on the ADT through which the main data is accessed,
rather than the way in which the data is encoded.  This allows more
freedom in the encoding of the main data.  In this paper, we present
succinct indexes for various data types, namely strings, binary
relations and multi-labeled trees.  Given the support for the
interface of the ADTs of these data types, we can support various
useful operations efficiently by constructing succinct indexes for
them.  When the operators in the ADTs are supported in constant time,
our results are comparable to previous results, while allowing more
flexibility in the encoding of the given data.

Using our techniques, we design the first succinct encoding that
represents a string of length $n$ over alphabet $[\sigma]$ using
$nH_k+o(n\log\sigma)$ bits that support access / rank / select operations in
$o((\log\log \sigma)^3)$ time.  We also design the first succinct text
index using $nH_k+o(n\log\sigma)$ bits that supports pattern matching
queries in $O(m\log\log\sigma + occ\log^{1+\epsilon}n\log\log\sigma)$ time,
for a given pattern of length $m$.  Previous results on these two
problems either have a $\log\sigma$ factor instead of $\log\log\sigma$ in
terms of running time, or are not compressible, but our results do not
have such problems.  More results are reported in the paper.
}  }


## 30 [CPM2006] "Adaptive Searching in Succinctly Encoded Binary Relations and Tree Structured Documents"   tTHEORY BIGDATA ADAPTIVE cConference

1. Authors
• Jérémy Barbay, Alexander Golynski, Ian J. Munro, Srinivasa Rao
3. Bibtex
@inproceedings{2006-CPM-AdaptiveSearchingInSuccinctlyEncodedBinaryRelationsAndTreeStructuredDocuments-BarbayGolynskiMunroRao,

author =       {J{\'e}r{\'e}my Barbay and Alexander Golynski and J. Ian Munro and S. Srinivasa Rao},
title =        {Adaptive Searching in Succinctly Encoded Binary Relations and Tree-Structured Documents},
booktitle =    cpm,
year =         2006,
pages =        {24-35},
series    = {Lecture Notes in Computer Science ({LNCS})},
volume    = 4009,
publisher =    {Springer-Verlag},
postscript =   {http://www.cs.uwaterloo.ca/~jbarbay/Recherche/Publishing/Publications/multiLabeledStringsAndTrees.ps},
pdf = {http://www.cs.uwaterloo.ca/~jbarbay/Recherche/Publishing/Publications/multiLabeledStringsAndTrees.pdf},
note =         {(Later extended in \cite{2007-TCS-AdaptiveSearchingInSuccinctlyEncodedBinaryRelationsAndTreeStructuredDocuments-BarbayGolynskiMunroRao})},
abstract = { The methods most heavily used by search engines to
answer conjunctive queries on binary relations (such as one
associating keywords with web pages) are based on computing the
intersection of inverted lists stored as sorted arrays and using
variants of binary search. We show that a succinct representation of
the binary relation permits much better results, while using less
space than traditional methods. We apply our results not only to
conjunctive queries on binary relations, but also to queries on
semi-structured documents such as XML documents or file-system
indexes, using a variant of an adaptive algorithm used to solve
conjunctive queries on binary relations.}  }


## 31 [WEA2006] "Faster Adaptive Set Intersections for Text Searching"   tSIMUL ADAPTIVE cConference

1. Authors
• Jérémy Barbay, Alez Lopez-Ortiz, Tyler Lu
3. Bibtex
@inproceedings{2006-WEA-FasterAdaptiveSetIntersectionsForTextSearching-BarbayLopezOrtizLu,
author =       {J{\'e}r{\'e}my Barbay and Alejandro L{\'o}pez-Ortiz and Tyler Lu},
title =        {Faster Adaptive Set Intersections for Text Searching},
booktitle = wea,
pages =        {146--157},
year =         2006,
DISABLEeditor =        {Carme Alvarez, Maria Serma },
volume =       4007,
series =       {Lecture Notes in Computer Science ({LNCS})},
publisher = {Springer Berlin / Heidelberg},
postscript =   {http://www.cs.uwaterloo.ca/~jbarbay/Recherche/Publishing/Publications/wea06.ps},
pdf = {http://www.cs.uwaterloo.ca/~jbarbay/Recherche/Publishing/Publications/wea06.pdf},
abstract = { The intersection of large ordered sets is a common
problem in the context of the evaluation of boolean queries to a
search engine. In this paper we engineer a better algorithm for this
task, which improves over those proposed by Demaine, Ian J. Munro and
L२pez-Ortiz [SODA 2000/ALENEX 2001], by using a variant of
interpolation search. More specifically, our contributions are
threefold. First, we coroborate and complete the practical study from
Demaine et al. on comparison based intersection algorithms. Second, we
show that in practice replacing Binary Search and galloping search by
a simple interpolation search improves the performance of each main
intersection algorithms. Third, we introduce and test variants of
interpolation search: this results in an even better intersection
algorithm.}  }


## 32 [TR2006a] "Adaptive Search Algorithm for Patterns in Succinctly Encoded XML"   tTHEORY ADAPTIVE cDraft

1. Authors
• Jérémy Barbay
2. Bibtex
@techreport{2006-TR-AdaptiveSearchAlgorithmForPatternsInSuccinctlyEncodedXML-Barbay,
author =      {J\'er\'emy Barbay},
title =       {Adaptive Search Algorithm for Patterns, in Succinctly Encoded {XML}},
institution =  {University of Waterloo, Ontario, Canada},
year =        2006,
key =         {CS-2006-11},
number =      {CS-2006-11}
}


## 33 [TR2006b] "Study of the Meiotic Recombination Hotspot Diffusion Paradox"   tSIMUL tTHEORY EVOLUTION cDraft

1. Authors
• Jérémy Barbay
2. Bibtex
@techreport{2006-TR-StudyOfTheMeioticRecombinationHotspotDiffusionParadox-Barbay,
author =      {J{\'e}r{\'e}my Barbay},
title =       {Study of the Meiotic Recombination Hotspot Diffusion Paradox},
institution =  {University of Waterloo},
year =        2006,
key =                 {CS-2006-38, }
}


## 34 [TR2006c] "Succinct Encoding for XPath Location Steps"   tTHEORY ADAPTIVE cDraft

1. Authors
• Jérémy Barbay, Srinivasa Rao
2. Bibtex
@techreport{2006-TR-SuccinctEncodingForXPathLocationSteps-BarbayRao,
author =      {J\'er\'emy Barbay and Srinivasa Rao},
title =       {Succinct Encoding for {XPath} Location Steps },
institution =  {University of Waterloo, Ontario, Canada},
year =        2006,
key =         {CS-2006-10},
number =      {CS-2006-10}
}


## 35 [Chapter2005] "Algorithmes Probabilistes"   PEDAGOGY cChapter

1. Authors
• Jérémy Barbay
3. Bibtex
@incollection{2005-Chapter-AlgorithmesProbabilistes-Barbay,
author =       {J़{\'e}r{\'e}़my Barbay},
title =        {Algorithmes Probabilistes},
booktitle =    {Optimisation Combinatoire : Concepts Fondamentaux},
publisher =    {Herm\es},
year =         2005,
pages =        {21-38},
editor =       {Vangelis Th. Paschos},
chapter =      2,
}


## 36 [Havana2004] "On the Use of a Computer to Teach More and Better in a Collective Manner"   tSIMUL PEDAGOGY cConference

1. Authors
• Jérémy Barbay
3. Bibtex
@inproceedings{2004-Havana-onTheUseOfAComputerToTeachMoreAndBetterInACollectiveManner-Barbay,
author =      {J{\'e}r{\'e}my Barbay},
title =       {On the Use of a Computer, to Teach More and Better, in a Collective Manner},
booktitle = {X International Convention of Computer Sciences of Havana (INFORMATICA 2004)},
year =        2004,
OPTmonth =    {May},
pdf = {http://www.cs.uwaterloo.ca/~jbarbay/Recherche/Publishing/Preprints/informatica2004.pdf},
abstract = {The use of computers to help teaching overcomes a fast
development. One of the main objectives is to teach isolated people
who can't join regular university courses. We show in this paper that
computers can be used to efficiently teach in a classroom without the
need of modern and expenseive equipement for students. The paper is
divided in two parts: in the first part we expose the principles,
results and evaluation of two experiments performed in parallel during
the teaching of a one-term fourth year undergrad course. In the second
part we expose how those two techniques can be extended in a single
more general technique, by using XML to define and manipulate a
general purpose database of solved problems; and how such a database
can be built in a dynamic and collective way.}  }


## 37 [TR2004] "Index Trees for Descendant Tree Queries in the Comparison Model"   tTHEORY ADAPTIVE cDraft

1. Authors
• Jérémy Barbay
2. Bibtex
@techreport{2004-TR-IndexTreesForDescendantTreeQueriesInTheComparisonModel-Barbay,
author =       {J\'er\'emy Barbay},
title =        {Index-Trees for Descendant Tree Queries in the Comparison Model},
institution =  {University of British Columbia},
year =         {2004},
key =          {XML, Index, Fine Analysis, Alternation},
number =       {TR-2004-11},
month =        {July},
}


## 38 [ISAAC2003] "Deterministic Algorithm for the t-Threshold Set Problem"   tTHEORY ADAPTIVE cJournalProject cConference

1. Authors
• Jérémy Barbay, Claire Kenyon-Mathieu
3. Grants
4. Bibtex
@inproceedings{2003-ISAAC-DeterministicAlgorithmForTheTThresholdSetProblem-BarbayKenyon,
author    = {J{\'e}r{\'e}my Barbay and
Claire Kenyon},
title     = {Deterministic Algorithm for the t-Threshold Set Problem.},
booktitle = isaac,
pages     = {575-584},
publisher = {Springer},
series    = {Lecture Notes in Computer Science ({LNCS})},
volume    = 2906,
year      = 2003,
bibsource = {DBLP, http://dblp.uni-trier.de},
abstract = { Given k sorted arrays, the t-Threshold problem, which
is motivated by indexed search engines, consists of finding the
elements which are present in at least t of the arrays. We present a
new deterministic algorithm for it and prove that, asymptotically in
the sizes of the arrays, it is optimal in the alternation model used
to study adaptive algorithms. We define the Opt-Threshold problem as
finding the smallest non empty $t$-threshold set, which is equivalent
to find the largest t such that the t-threshold set is non empty, and
propose a naive algorithm to solve it.}  }


## 39 [SAGA2003] "Optimality Of Randomized Algorithms for the Intersection Problem"   tTHEORY ADAPTIVE cConference

1. Authors
• Jérémy Barbay
3. Bibtex
@inproceedings{2003-SAGA-OptimalityOfRandomizedAlgorithmsForTheIntersectionProblem-Barbay,
author =       {J{\'e}r{\'e}my Barbay},
title =        {Optimality of Randomized Algorithms for the Intersection Problem},
booktitle = saga,
pages =        {26--38},
year =         2003,
editor =       {Andreas Albrecht },
volume =       2827,
month =        {November},
series    = {Lecture Notes in Computer Science {(LNCS)}},
publisher = {Springer},
note = {(Later extended in \cite{2008-TALG-AlternationAndRedundancyAnalysisOfTheIntersectionProblem-BarbayKenyon})},
postscript =   {http://www.cs.uwaterloo.ca/~jbarbay/Recherche/Publishing/Publications/redundancy_saga.ps},
pdf = {http://www.cs.uwaterloo.ca/~jbarbay/Recherche/Publishing/Publications/redundancy_saga.pdf},
abstract = { The "Intersection of sorted arrays" problem has
applications in indexed search engines such as Google. Previous works
propose and compare deterministic algorithms for this problem, and
offer lower bounds on the randomized complexity in different models
(cost model, alternation model). We refine the alternation model into
the redundancy model to prove that randomized algorithms perform
better than deterministic ones on the intersection problem. We present
a randomized and simplified version of a previous algorithm, optimal
in this model.}  }


## 40 [PHD2002] "Analyse Fine Bornes Inferieures et Algorithmes de Calculs d'Intersection pour Moteurs de Recherche"   tTHEORY ADAPTIVE cThesis

1. Authors
• Jérémy Barbay
3. Authors
• Jérémy Barbay, Claire Kenyon-Mathieu

@phdthesis{2002-PhDThesis-AnalyseFineBornesInferieuresEtAlgorithmesDeCalculsDIntersectionPourMoteursDeRecherche-Barbay, author = {J{\'e}r{\'e}my Barbay}, title = {Analyse fine: bornes inf{\'e}rieures et algorithmes de calculs d'intersection pour moteurs de recherche }, school = {Universit{\'e} Paris-Sud}, year = 2002, address = {Laboratoire de Recherche en Informatique}, month = {Septembre}, } #+ENDSRC

1. Authors
• Jérémy Barbay, Claire Kenyon-Mathieu
3. Bibtex
@inproceedings{2002-SODA-AdaptiveIntersectionAndTThresholdProblems-BarbayKenyon,
author =       {J{\'e}r{\'e}my Barbay and Claire Kenyon},
title =        {Adaptive Intersection and t-Threshold Problems},
booktitle =    soda,
key =          {Adaptive Algorithms, Random Lower Bounds},
pages =        {390--399},
year =         2002,
month =        {January},
publisher = {Society for Industrial and Applied Mathematics (SIAM)},
abstract = {Consider the problem of computing the intersection of k
sorted sets. In the comparison model, we prove a new lower bound which
depends on the non-deterministic complexity of the instance, and
implies that the algorithm of Demaine, L२pez-Ortiz and Munro is
usually optimal in this adaptive'' sense. We extend the lower bound
and the algorithm to the t-Threshold Problem, which consists in
finding the elements which are in at least t of the k sets. These
problems are motivated by boolean queries in text database systems.}
}


## 42 [SODA2001] "On the Discrete Bak Sneppen Model"   tSIMUL tTHEORY EVOLUTION cConference

1. Authors
• Jérémy Barbay, Claire Kenyon-Mathieu
3. Bibtex
@inproceedings{2001-SODA-OnTheDiscreteBakSneppenModel-BarbayKenyon,
author =       {J{\'e}r{\'e}my Barbay  and Claire Kenyon},
title =        {On the Discrete {Bak-Sneppen} Model},
booktitle =    soda,
key =          {Self Organized Criticality, {Bak Sneppen}, Percolation},
pages =        {928--931},
year =         2001,
month =        {January},
organization = {ACM-SIAM},
publisher = {ACM},
postscript =   {http://www.cs.uwaterloo.ca/~jbarbay/Recherche/Publishing/Publications/evol.ps},
pdf =   {http://www.cs.uwaterloo.ca/~jbarbay/Recherche/Publishing/Publications/evol.pdf},
abstract = { We propose a discrete variant of the {Bak-Sneppen} model
for self-organized criticality. In this process, a configuration is an
n-bit word, and at each step one chooses a random bit of minimum value
(usually a zero) and replaces it and its two neighbors by independent
Bernoulli variables with parameter p. We prove bounds on the average
number of ones in the stationary distribution and present experimental
results.}
}


## 43 [ParisSud2000] "Les etudiants ont le sens du protocole"   tSIMUL cPopular

1. Authors
• Jérémy Barbay
• 2000-ParisSud-FFSS-Barbay.pdf

## 44 [MASTER1998] "Capacités d'Adaptation des Algorithmes Génétiques"   tSIMUL EVOLUTION cThesis

1. Authors
• Jérémy Barbay
2. Bibtex
@mastersthesis{1998-MasterThesis-CapacitesDAdaptationDesAlgorithmesGenetiques-Barbay,
author = {J\'er\'emy Barbay},
title = {Capacit\'es d'adaptation des Algorithmes G\'en\'etiques},
school = {Universit\'e Paris-Sud, France},
year = {1998},
month = {Aout},
note = {Sous la direction d'Antoine Cornu\'ejols et d'Yves Kodratoff},
annote = {Int\'eressant seulement {\a} titre d'exemple.},
postscript = {http://www.lri.fr/~jeremy/bib/1998/rapport_stage.ps.gz}
}