12 Search Results for "J�gu, Victor"

Document
DOI: 10.4230/LIPIcs.ESA.2023.30
New Menger-Like Dualities in Digraphs and Applications to Half-Integral Linkages

Authors: Victor Campos, Jonas Costa, Raul Lopes, and Ignasi Sau

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
We present new min-max relations in digraphs between the number of paths satisfying certain conditions and the order of the corresponding cuts. We define these objects in order to capture, in the context of solving the half-integral linkage problem, the essential properties needed for reaching a large bramble of congestion two (or any other constant) from the terminal set. This strategy has been used ad-hoc in several articles, usually with lengthy technical proofs, and our objective is to abstract it to make it applicable in a simpler and unified way. We provide two proofs of the min-max relations, one consisting in applying Menger’s Theorem on appropriately defined auxiliary digraphs, and an alternative simpler one using matroids, however with worse polynomial running time. As an application, we manage to simplify and improve several results of Edwards et al. [ESA 2017] and of Giannopoulou et al. [SODA 2022] about finding half-integral linkages in digraphs. Concerning the former, besides being simpler, our proof provides an almost optimal bound on the strong connectivity of a digraph for it to be half-integrally feasible under the presence of a large bramble of congestion two (or equivalently, if the directed tree-width is large, which is the hard case). Concerning the latter, our proof uses brambles as rerouting objects instead of cylindrical grids, hence yielding much better bounds and being somehow independent of a particular topology. We hope that our min-max relations will find further applications as, in our opinion, they are simple, robust, and versatile to be easily applicable to different types of routing problems in digraphs.
Cite as

Victor Campos, Jonas Costa, Raul Lopes, and Ignasi Sau. New Menger-Like Dualities in Digraphs and Applications to Half-Integral Linkages. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{campos_et_al:LIPIcs.ESA.2023.30,
  author =	{Campos, Victor and Costa, Jonas and Lopes, Raul and Sau, Ignasi},
  title =	{{New Menger-Like Dualities in Digraphs and Applications to Half-Integral Linkages}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{30:1--30:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.30},
  URN =		{urn:nbn:de:0030-drops-186838},
  doi =		{10.4230/LIPIcs.ESA.2023.30},
  annote =	{Keywords: directed graphs, min-max relation, half-integral linkage, directed disjoint paths, bramble, parameterized complexity, matroids}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.31
Sample Compression Schemes for Balls in Graphs

Authors: Jérémie Chalopin, Victor Chepoi, Fionn Mc Inerney, Sébastien Ratel, and Yann Vaxès

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
One of the open problems in machine learning is whether any set-family of VC-dimension d admits a sample compression scheme of size O(d). In this paper, we study this problem for balls in graphs. For balls of arbitrary radius r, we design proper sample compression schemes of size 4 for interval graphs, of size 6 for trees of cycles, and of size 22 for cube-free median graphs. We also design approximate sample compression schemes of size 2 for balls of δ-hyperbolic graphs.
Cite as

Jérémie Chalopin, Victor Chepoi, Fionn Mc Inerney, Sébastien Ratel, and Yann Vaxès. Sample Compression Schemes for Balls in Graphs. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chalopin_et_al:LIPIcs.MFCS.2022.31,
  author =	{Chalopin, J\'{e}r\'{e}mie and Chepoi, Victor and Mc Inerney, Fionn and Ratel, S\'{e}bastien and Vax\`{e}s, Yann},
  title =	{{Sample Compression Schemes for Balls in Graphs}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.31},
  URN =		{urn:nbn:de:0030-drops-168298},
  doi =		{10.4230/LIPIcs.MFCS.2022.31},
  annote =	{Keywords: Proper Sample Compression Schemes, Balls, Graphs, VC-dimension}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2021.4
A New Framework for Kernelization Lower Bounds: The Case of Maximum Minimal Vertex Cover

Authors: Júlio Araújo, Marin Bougeret, Victor Campos, and Ignasi Sau

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

Abstract
In the Maximum Minimal Vertex Cover (MMVC) problem, we are given a graph G and a positive integer k, and the objective is to decide whether G contains a minimal vertex cover of size at least k. Motivated by the kernelization of MMVC with parameter k, our main contribution is to introduce a simple general framework to obtain lower bounds on the degrees of a certain type of polynomial kernels for vertex-optimization problems, which we call {lop-kernels}. Informally, this type of kernels is required to preserve large optimal solutions in the reduced instance, and captures the vast majority of existing kernels in the literature. As a consequence of this framework, we show that the trivial quadratic kernel for MMVC is essentially optimal, answering a question of Boria et al. [Discret. Appl. Math. 2015], and that the known cubic kernel for Maximum Minimal Feedback Vertex Set is also essentially optimal. On the positive side, given the (plausible) non-existence of subquadratic kernels for MMVC on general graphs, we provide subquadratic kernels on H-free graphs for several graphs H, such as the bull, the paw, or the complete graphs, by making use of the Erdős-Hajnal property in order to find an appropriate decomposition. Finally, we prove that MMVC does not admit polynomial kernels parameterized by the size of a minimum vertex cover of the input graph, even on bipartite graphs, unless NP ⊆ coNP / poly. This indicates that parameters smaller than the solution size are unlike to yield polynomial kernels for MMVC.
Cite as

Júlio Araújo, Marin Bougeret, Victor Campos, and Ignasi Sau. A New Framework for Kernelization Lower Bounds: The Case of Maximum Minimal Vertex Cover. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{araujo_et_al:LIPIcs.IPEC.2021.4,
  author =	{Ara\'{u}jo, J\'{u}lio and Bougeret, Marin and Campos, Victor and Sau, Ignasi},
  title =	{{A New Framework for Kernelization Lower Bounds: The Case of Maximum Minimal Vertex Cover}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{4:1--4:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.4},
  URN =		{urn:nbn:de:0030-drops-153879},
  doi =		{10.4230/LIPIcs.IPEC.2021.4},
  annote =	{Keywords: Maximum minimal vertex cover, parameterized complexity, polynomial kernel, kernelization lower bound, Erd\H{o}s-Hajnal property, induced subgraphs}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.27
Fractional Homomorphism, Weisfeiler-Leman Invariance, and the Sherali-Adams Hierarchy for the Constraint Satisfaction Problem

Authors: Silvia Butti and Víctor Dalmau

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
Given a pair of graphs 𝐀 and 𝐁, the problems of deciding whether there exists either a homomorphism or an isomorphism from 𝐀 to 𝐁 have received a lot of attention. While graph homomorphism is known to be NP-complete, the complexity of the graph isomorphism problem is not fully understood. A well-known combinatorial heuristic for graph isomorphism is the Weisfeiler-Leman test together with its higher order variants. On the other hand, both problems can be reformulated as integer programs and various LP methods can be applied to obtain high-quality relaxations that can still be solved efficiently. We study so-called fractional relaxations of these programs in the more general context where 𝐀 and 𝐁 are not graphs but arbitrary relational structures. We give a combinatorial characterization of the Sherali-Adams hierarchy applied to the homomorphism problem in terms of fractional isomorphism. Collaterally, we also extend a number of known results from graph theory to give a characterization of the notion of fractional isomorphism for relational structures in terms of the Weisfeiler-Leman test, equitable partitions, and counting homomorphisms from trees. As a result, we obtain a description of the families of CSPs that are closed under Weisfeiler-Leman invariance in terms of their polymorphisms as well as decidability by the first level of the Sherali-Adams hierarchy.
Cite as

Silvia Butti and Víctor Dalmau. Fractional Homomorphism, Weisfeiler-Leman Invariance, and the Sherali-Adams Hierarchy for the Constraint Satisfaction Problem. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 27:1-27:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{butti_et_al:LIPIcs.MFCS.2021.27,
  author =	{Butti, Silvia and Dalmau, V{\'\i}ctor},
  title =	{{Fractional Homomorphism, Weisfeiler-Leman Invariance, and the Sherali-Adams Hierarchy for the Constraint Satisfaction Problem}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{27:1--27:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.27},
  URN =		{urn:nbn:de:0030-drops-144679},
  doi =		{10.4230/LIPIcs.MFCS.2021.27},
  annote =	{Keywords: Weisfeiler-Leman algorithm, Sherali-Adams hierarchy, Graph homomorphism, Constraint Satisfaction Problem}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.10
Medians in Median Graphs and Their Cube Complexes in Linear Time

Authors: Laurine Bénéteau, Jérémie Chalopin, Victor Chepoi, and Yann Vaxès

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
The median of a set of vertices P of a graph G is the set of all vertices x of G minimizing the sum of distances from x to all vertices of P. In this paper, we present a linear time algorithm to compute medians in median graphs, improving over the existing quadratic time algorithm. We also present a linear time algorithm to compute medians in the 𝓁₁-cube complexes associated with median graphs. Median graphs constitute the principal class of graphs investigated in metric graph theory and have a rich geometric and combinatorial structure. Our algorithm is based on the majority rule characterization of medians in median graphs and on a fast computation of parallelism classes of edges (Θ-classes or hyperplanes) via Lexicographic Breadth First Search (LexBFS). To prove the correctness of our algorithm, we show that any LexBFS ordering of the vertices of G satisfies the following fellow traveler property of independent interest: the parents of any two adjacent vertices of G are also adjacent.
Cite as

Laurine Bénéteau, Jérémie Chalopin, Victor Chepoi, and Yann Vaxès. Medians in Median Graphs and Their Cube Complexes in Linear Time. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{beneteau_et_al:LIPIcs.ICALP.2020.10,
  author =	{B\'{e}n\'{e}teau, Laurine and Chalopin, J\'{e}r\'{e}mie and Chepoi, Victor and Vax\`{e}s, Yann},
  title =	{{Medians in Median Graphs and Their Cube Complexes in Linear Time}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{10:1--10:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.10},
  URN =		{urn:nbn:de:0030-drops-124171},
  doi =		{10.4230/LIPIcs.ICALP.2020.10},
  annote =	{Keywords: Median Graph, CAT(0) Cube Complex, Median Problem, Linear Time Algorithm, LexBFS}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.34
Unlabeled Sample Compression Schemes and Corner Peelings for Ample and Maximum Classes

Authors: Jérémie Chalopin, Victor Chepoi, Shay Moran, and Manfred K. Warmuth

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
We examine connections between combinatorial notions that arise in machine learning and topological notions in cubical/simplicial geometry. These connections enable to export results from geometry to machine learning. Our first main result is based on a geometric construction by H. Tracy Hall (2004) of a partial shelling of the cross-polytope which can not be extended. We use it to derive a maximum class of VC dimension 3 that has no corners. This refutes several previous works in machine learning from the past 11 years. In particular, it implies that the previous constructions of optimal unlabeled compression schemes for maximum classes are erroneous. On the positive side we present a new construction of an optimal unlabeled compression scheme for maximum classes. We leave as open whether our unlabeled compression scheme extends to ample (a.k.a. lopsided or extremal) classes, which represent a natural and far-reaching generalization of maximum classes. Towards resolving this question, we provide a geometric characterization in terms of unique sink orientations of the 1-skeletons of associated cubical complexes.
Cite as

Jérémie Chalopin, Victor Chepoi, Shay Moran, and Manfred K. Warmuth. Unlabeled Sample Compression Schemes and Corner Peelings for Ample and Maximum Classes. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chalopin_et_al:LIPIcs.ICALP.2019.34,
  author =	{Chalopin, J\'{e}r\'{e}mie and Chepoi, Victor and Moran, Shay and Warmuth, Manfred K.},
  title =	{{Unlabeled Sample Compression Schemes and Corner Peelings for Ample and Maximum Classes}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.34},
  URN =		{urn:nbn:de:0030-drops-106105},
  doi =		{10.4230/LIPIcs.ICALP.2019.34},
  annote =	{Keywords: VC-dimension, sample compression, Sauer-Shelah-Perles lemma, Sandwich lemma, maximum class, ample/extremal class, corner peeling, unique sink orientation}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2018.12
Dual Parameterization of Weighted Coloring

Authors: Júlio Araújo, Victor A. Campos, Carlos Vinícius G. C. Lima, Vinícius Fernandes dos Santos, Ignasi Sau, and Ana Silva

Published in: LIPIcs, Volume 115, 13th International Symposium on Parameterized and Exact Computation (IPEC 2018)

Abstract
Given a graph G, a proper k-coloring of G is a partition c = (S_i)_{i in [1,k]} of V(G) into k stable sets S_1,..., S_k. Given a weight function w: V(G) -> R^+, the weight of a color S_i is defined as w(i) = max_{v in S_i} w(v) and the weight of a coloring c as w(c) = sum_{i=1}^{k} w(i). Guan and Zhu [Inf. Process. Lett., 1997] defined the weighted chromatic number of a pair (G,w), denoted by sigma(G,w), as the minimum weight of a proper coloring of G. The problem of determining sigma(G,w) has received considerable attention during the last years, and has been proved to be notoriously hard: for instance, it is NP-hard on split graphs, unsolvable on n-vertex trees in time n^{o(log n)} unless the ETH fails, and W[1]-hard on forests parameterized by the size of a largest tree. We focus on the so-called dual parameterization of the problem: given a vertex-weighted graph (G,w) and an integer k, is sigma(G,w) <= sum_{v in V(G)} w(v) - k? This parameterization has been recently considered by Escoffier [WG, 2016], who provided an FPT algorithm running in time 2^{O(k log k)} * n^{O(1)}, and asked which kernel size can be achieved for the problem. We provide an FPT algorithm running in time 9^k * n^{O(1)}, and prove that no algorithm in time 2^{o(k)} * n^{O(1)} exists under the ETH. On the other hand, we present a kernel with at most (2^{k-1}+1) (k-1) vertices, and rule out the existence of polynomial kernels unless NP subseteq coNP/poly, even on split graphs with only two different weights. Finally, we identify some classes of graphs on which the problem admits a polynomial kernel, in particular interval graphs and subclasses of split graphs, and in the latter case we present lower bounds on the degrees of the polynomials.
Cite as

Júlio Araújo, Victor A. Campos, Carlos Vinícius G. C. Lima, Vinícius Fernandes dos Santos, Ignasi Sau, and Ana Silva. Dual Parameterization of Weighted Coloring. In 13th International Symposium on Parameterized and Exact Computation (IPEC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 115, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{araujo_et_al:LIPIcs.IPEC.2018.12,
  author =	{Ara\'{u}jo, J\'{u}lio and Campos, Victor A. and Lima, Carlos Vin{\'\i}cius G. C. and Fernandes dos Santos, Vin{\'\i}cius and Sau, Ignasi and Silva, Ana},
  title =	{{Dual Parameterization of Weighted Coloring}},
  booktitle =	{13th International Symposium on Parameterized and Exact Computation (IPEC 2018)},
  pages =	{12:1--12:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-084-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{115},
  editor =	{Paul, Christophe and Pilipczuk, Michal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2018.12},
  URN =		{urn:nbn:de:0030-drops-102134},
  doi =		{10.4230/LIPIcs.IPEC.2018.12},
  annote =	{Keywords: weighted coloring, max coloring, parameterized complexity, dual parameterization, FPT algorithms, polynomial kernels, split graphs, interval graphs}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2018.22
Fast Approximation and Exact Computation of Negative Curvature Parameters of Graphs

Authors: Jérémie Chalopin, Victor Chepoi, Feodor F. Dragan, Guillaume Ducoffe, Abdulhakeem Mohammed, and Yann Vaxès

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

Abstract
In this paper, we study Gromov hyperbolicity and related parameters, that represent how close (locally) a metric space is to a tree from a metric point of view. The study of Gromov hyperbolicity for geodesic metric spaces can be reduced to the study of graph hyperbolicity. Our main contribution in this note is a new characterization of hyperbolicity for graphs (and for complete geodesic metric spaces). This characterization has algorithmic implications in the field of large-scale network analysis, which was one of our initial motivations. A sharp estimate of graph hyperbolicity is useful, {e.g.}, in embedding an undirected graph into hyperbolic space with minimum distortion [Verbeek and Suri, SoCG'14]. The hyperbolicity of a graph can be computed in polynomial-time, however it is unlikely that it can be done in subcubic time. This makes this parameter difficult to compute or to approximate on large graphs. Using our new characterization of graph hyperbolicity, we provide a simple factor 8 approximation algorithm for computing the hyperbolicity of an n-vertex graph G=(V,E) in optimal time O(n^2) (assuming that the input is the distance matrix of the graph). This algorithm leads to constant factor approximations of other graph-parameters related to hyperbolicity (thinness, slimness, and insize). We also present the first efficient algorithms for exact computation of these parameters. All of our algorithms can be used to approximate the hyperbolicity of a geodesic metric space.
Cite as

Jérémie Chalopin, Victor Chepoi, Feodor F. Dragan, Guillaume Ducoffe, Abdulhakeem Mohammed, and Yann Vaxès. Fast Approximation and Exact Computation of Negative Curvature Parameters of Graphs. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 22:1-22:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chalopin_et_al:LIPIcs.SoCG.2018.22,
  author =	{Chalopin, J\'{e}r\'{e}mie and Chepoi, Victor and Dragan, Feodor F. and Ducoffe, Guillaume and Mohammed, Abdulhakeem and Vax\`{e}s, Yann},
  title =	{{Fast Approximation and Exact Computation of Negative Curvature Parameters of Graphs}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{22:1--22:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.22},
  URN =		{urn:nbn:de:0030-drops-87356},
  doi =		{10.4230/LIPIcs.SoCG.2018.22},
  annote =	{Keywords: Gromov hyperbolicity, Graphs, Geodesic metric spaces, Approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2018.43
Differential Privacy on Finite Computers

Authors: Victor Balcer and Salil Vadhan

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract
We consider the problem of designing and analyzing differentially private algorithms that can be implemented on discrete models of computation in strict polynomial time, motivated by known attacks on floating point implementations of real-arithmetic differentially private algorithms (Mironov, CCS 2012) and the potential for timing attacks on expected polynomial-time algorithms. We use a case study: the basic problem of approximating the histogram of a categorical dataset over a possibly large data universe X. The classic Laplace Mechanism (Dwork, McSherry, Nissim, Smith, TCC 2006 and J. Privacy & Confidentiality 2017) does not satisfy our requirements, as it is based on real arithmetic, and natural discrete analogues, such as the Geometric Mechanism (Ghosh, Roughgarden, Sundarajan, STOC 2009 and SICOMP 2012), take time at least linear in |X|, which can be exponential in the bit length of the input. In this paper, we provide strict polynomial-time discrete algorithms for approximate histograms whose simultaneous accuracy (the maximum error over all bins) matches that of the Laplace Mechanism up to constant factors, while retaining the same (pure) differential privacy guarantee. One of our algorithms produces a sparse histogram as output. Its "per-bin accuracy" (the error on individual bins) is worse than that of the Laplace Mechanism by a factor of log |X|, but we prove a lower bound showing that this is necessary for any algorithm that produces a sparse histogram. A second algorithm avoids this lower bound, and matches the per-bin accuracy of the Laplace Mechanism, by producing a compact and efficiently computable representation of a dense histogram; it is based on an (n+1)-wise independent implementation of an appropriately clamped version of the Discrete Geometric Mechanism.
Cite as

Victor Balcer and Salil Vadhan. Differential Privacy on Finite Computers. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 43:1-43:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{balcer_et_al:LIPIcs.ITCS.2018.43,
  author =	{Balcer, Victor and Vadhan, Salil},
  title =	{{Differential Privacy on Finite Computers}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{43:1--43:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.43},
  URN =		{urn:nbn:de:0030-drops-83537},
  doi =		{10.4230/LIPIcs.ITCS.2018.43},
  annote =	{Keywords: Algorithms, Differential Privacy, Discrete Computation, Histograms}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.101
A Counterexample to Thiagarajan's Conjecture on Regular Event Structures

Authors: Jérémie Chalopin and Victor Chepoi

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
We provide a counterexample to a conjecture by Thiagarajan (1996 and 2002) that regular prime event structures correspond exactly to those obtained as unfoldings of finite 1-safe Petri nets. The same counterexample is used to disprove a closely related conjecture by Badouel, Darondeau, and Raoult (1999) that domains of regular event structures with bounded natural-cliques are recognizable by finite trace automata. Event structures, trace automata, and Petri nets are fundamental models in concurrency theory. There exist nice interpretations of these structures as combinatorial and geometric objects and both conjectures can be reformulated in this framework. Namely, the domains of prime event structures correspond exactly to pointed median graphs; from a geometric point of view, these domains are in bijection with pointed CAT(0) cube complexes. A necessary condition for both conjectures to be true is that domains of respective regular event structures admit a regular nice labeling. To disprove these conjectures, we describe a regular event domain (with bounded natural-cliques) that does not admit a regular nice labeling. Our counterexample is derived from an example by Wise (1996 and 2007) of a nonpositively curved square complex whose universal cover is a CAT(0) square complex containing a particular plane with an aperiodic tiling.
Cite as

Jérémie Chalopin and Victor Chepoi. A Counterexample to Thiagarajan's Conjecture on Regular Event Structures. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 101:1-101:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chalopin_et_al:LIPIcs.ICALP.2017.101,
  author =	{Chalopin, J\'{e}r\'{e}mie and Chepoi, Victor},
  title =	{{A Counterexample to Thiagarajan's Conjecture  on Regular Event Structures}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{101:1--101:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.101},
  URN =		{urn:nbn:de:0030-drops-74192},
  doi =		{10.4230/LIPIcs.ICALP.2017.101},
  annote =	{Keywords: Discrete event structures, Trace automata, Median graphs and CAT(0) cube Complexes, Unfoldings and universal covers}
}
Document
DOI: 10.4230/OASIcs.WCET.2005.810
Computing the Worst Case Execution Time of an Avionics Program by Abstract Interpretation

Authors: Jean Souyris, Erwan Le Pavec, Guillaume Himbert, Guillaume Borios, Victor Jégu, and Reinhold Heckmann

Published in: OASIcs, Volume 1, 5th International Workshop on Worst-Case Execution Time Analysis (WCET'05) (2007)

Abstract
This paper presents how the timing analyser aiT is used for computing the Worst-Case Execution Time (WCET) of two safety-critical avionics programs. The aiT tool has been developed by AbsInt GmbH as a static analyser based on Abstract Interpretation
Cite as

Jean Souyris, Erwan Le Pavec, Guillaume Himbert, Guillaume Borios, Victor Jégu, and Reinhold Heckmann. Computing the Worst Case Execution Time of an Avionics Program by Abstract Interpretation. In 5th International Workshop on Worst-Case Execution Time Analysis (WCET'05). Open Access Series in Informatics (OASIcs), Volume 1, pp. 21-24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{souyris_et_al:OASIcs.WCET.2005.810,
  author =	{Souyris, Jean and Le Pavec, Erwan and Himbert, Guillaume and Borios, Guillaume and J\'{e}gu, Victor and Heckmann, Reinhold},
  title =	{{Computing the Worst Case Execution Time of an Avionics Program by Abstract Interpretation}},
  booktitle =	{5th International Workshop on Worst-Case Execution Time Analysis (WCET'05)},
  pages =	{21--24},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-24-8},
  ISSN =	{2190-6807},
  year =	{2008},
  volume =	{1},
  editor =	{Wilhelm, Reinhard},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.WCET.2005.810},
  URN =		{urn:nbn:de:0030-drops-8103},
  doi =		{10.4230/OASIcs.WCET.2005.810},
  annote =	{Keywords: }
}
Document
DOI: 10.4230/DagSemProc.07462.12
Functional Changes in Older Adults: Impact on Home Technology Design

Authors: Victor A. Hirth

Published in: Dagstuhl Seminar Proceedings, Volume 7462, Assisted Living Systems - Models, Architectures and Engineering Approaches (2008)

Abstract
The aging demographic being experienced by all western countries has significant impact on health care utilization as well as the ability to remain in independent living situations. Chronic medical conditions and functional disability impair older adults’ ability to remain independent. Ambient assisted living technologies may help less the burden of disability and increase the likelihood of older adults remaining independent into their later years.
Cite as

Victor A. Hirth. Functional Changes in Older Adults: Impact on Home Technology Design. In Assisted Living Systems - Models, Architectures and Engineering Approaches. Dagstuhl Seminar Proceedings, Volume 7462, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{hirth:DagSemProc.07462.12,
  author =	{Hirth, Victor A.},
  title =	{{Functional Changes in Older Adults:  Impact on Home Technology Design}},
  booktitle =	{Assisted Living Systems - Models, Architectures and Engineering Approaches},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7462},
  editor =	{Arthur I. Karshmer and J\"{u}rgen Nehmer and Hartmut Raffler and Gerhard Tr\"{o}ster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07462.12},
  URN =		{urn:nbn:de:0030-drops-14619},
  doi =		{10.4230/DagSemProc.07462.12},
  annote =	{Keywords: Chronic disease, functional and cognitive decline, geriatric syndromes}
}
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