12 Search Results for "Nešetřil, Jaroslav"

Document
DOI: 10.4230/LIPIcs.SEA.2024.6
Faster Treewidth-Based Approximations for Wiener Index

Authors: Giovanna Kobus Conrado, Amir Kafshdar Goharshady, Pavel Hudec, Pingjiang Li, and Harshit Jitendra Motwani

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
The Wiener index of a graph G is the sum of distances between all pairs of its vertices. It is a widely-used graph property in chemistry, initially introduced to examine the link between boiling points and structural properties of alkanes, which later found notable applications in drug design. Thus, computing or approximating the Wiener index of molecular graphs, i.e. graphs in which every vertex models an atom of a molecule and every edge models a bond, is of significant interest to the computational chemistry community. In this work, we build upon the observation that molecular graphs are sparse and tree-like and focus on developing efficient algorithms parameterized by treewidth to approximate the Wiener index. We present a new randomized approximation algorithm using a combination of tree decompositions and centroid decompositions. Our algorithm approximates the Wiener index within any desired multiplicative factor (1 ± ε) in time O(n ⋅ log n ⋅ k³ + √n ⋅ k/ε²), where n is the number of vertices of the graph and k is the treewidth. This time bound is almost-linear in n. Finally, we provide experimental results over standard benchmark molecules from PubChem and the Protein Data Bank, showcasing the applicability and scalability of our approach on real-world chemical graphs and comparing it with previous methods.
Cite as

Giovanna Kobus Conrado, Amir Kafshdar Goharshady, Pavel Hudec, Pingjiang Li, and Harshit Jitendra Motwani. Faster Treewidth-Based Approximations for Wiener Index. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{conrado_et_al:LIPIcs.SEA.2024.6,
  author =	{Conrado, Giovanna Kobus and Goharshady, Amir Kafshdar and Hudec, Pavel and Li, Pingjiang and Motwani, Harshit Jitendra},
  title =	{{Faster Treewidth-Based Approximations for Wiener Index}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.6},
  URN =		{urn:nbn:de:0030-drops-203718},
  doi =		{10.4230/LIPIcs.SEA.2024.6},
  annote =	{Keywords: Computational Chemistry, Treewidth, Wiener Index}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.37
Fast Approximate Counting of Cycles

Authors: Keren Censor-Hillel, Tomer Even, and Virginia Vassilevska Williams

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We consider the problem of approximate counting of triangles and longer fixed length cycles in directed graphs. For triangles, Tětek [ICALP'22] gave an algorithm that returns a (1±ε)-approximation in Õ(n^ω/t^{ω-2}) time, where t is the unknown number of triangles in the given n node graph and ω < 2.372 is the matrix multiplication exponent. We obtain an improved algorithm whose running time is, within polylogarithmic factors the same as that for multiplying an n× n/t matrix by an n/t × n matrix. We then extend our framework to obtain the first nontrivial (1± ε)-approximation algorithms for the number of h-cycles in a graph, for any constant h ≥ 3. Our running time is Õ(MM(n,n/t^{1/(h-2)},n)), the time to multiply n × n/(t^{1/(h-2)}) by n/(t^{1/(h-2)) × n matrices. Finally, we show that under popular fine-grained hypotheses, this running time is optimal.
Cite as

Keren Censor-Hillel, Tomer Even, and Virginia Vassilevska Williams. Fast Approximate Counting of Cycles. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 37:1-37:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{censorhillel_et_al:LIPIcs.ICALP.2024.37,
  author =	{Censor-Hillel, Keren and Even, Tomer and Vassilevska Williams, Virginia},
  title =	{{Fast Approximate Counting of Cycles}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{37:1--37:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.37},
  URN =		{urn:nbn:de:0030-drops-201809},
  doi =		{10.4230/LIPIcs.ICALP.2024.37},
  annote =	{Keywords: Approximate triangle counting, Approximate cycle counting Fast matrix multiplication, Fast rectangular matrix multiplication}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.68
A Tight Subexponential-Time Algorithm for Two-Page Book Embedding

Authors: Robert Ganian, Haiko Müller, Sebastian Ordyniak, Giacomo Paesani, and Mateusz Rychlicki

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
A book embedding of a graph is a drawing that maps vertices onto a line and edges to simple pairwise non-crossing curves drawn into "pages", which are half-planes bounded by that line. Two-page book embeddings, i.e., book embeddings into 2 pages, are of special importance as they are both NP-hard to compute and have specific applications. We obtain a 2^𝒪(√n) algorithm for computing a book embedding of an n-vertex graph on two pages - a result which is asymptotically tight under the Exponential Time Hypothesis. As a key tool in our approach, we obtain a single-exponential fixed-parameter algorithm for the same problem when parameterized by the treewidth of the input graph. We conclude by establishing the fixed-parameter tractability of computing minimum-page book embeddings when parameterized by the feedback edge number, settling an open question arising from previous work on the problem.
Cite as

Robert Ganian, Haiko Müller, Sebastian Ordyniak, Giacomo Paesani, and Mateusz Rychlicki. A Tight Subexponential-Time Algorithm for Two-Page Book Embedding. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 68:1-68:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{ganian_et_al:LIPIcs.ICALP.2024.68,
  author =	{Ganian, Robert and M\"{u}ller, Haiko and Ordyniak, Sebastian and Paesani, Giacomo and Rychlicki, Mateusz},
  title =	{{A Tight Subexponential-Time Algorithm for Two-Page Book Embedding}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{68:1--68:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.68},
  URN =		{urn:nbn:de:0030-drops-202114},
  doi =		{10.4230/LIPIcs.ICALP.2024.68},
  annote =	{Keywords: book embedding, page number, subexponential algorithms, subhamiltonicity, feedback edge number}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.77
Towards Tight Bounds for the Graph Homomorphism Problem Parameterized by Cutwidth via Asymptotic Matrix Parameters

Authors: Carla Groenland, Isja Mannens, Jesper Nederlof, Marta Piecyk, and Paweł Rzążewski

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
A homomorphism from a graph G to a graph H is an edge-preserving mapping from V(G) to V(H). In the graph homomorphism problem, denoted by Hom(H), the graph H is fixed and we need to determine if there exists a homomorphism from an instance graph G to H. We study the complexity of the problem parameterized by the cutwidth of G, i.e., we assume that G is given along with a linear ordering v_1,…,v_n of V(G) such that, for each i ∈ {1,…,n-1}, the number of edges with one endpoint in {v_1,…,v_i} and the other in {v_{i+1},…,v_n} is at most k. We aim, for each H, for algorithms for Hom(H) running in time c_H^k n^𝒪(1) and matching lower bounds that exclude c_H^{k⋅o(1)} n^𝒪(1) or c_H^{k(1-Ω(1))} n^𝒪(1) time algorithms under the (Strong) Exponential Time Hypothesis. In the paper we introduce a new parameter that we call mimsup(H). Our main contribution is strong evidence of a close connection between c_H and mimsup(H): - an information-theoretic argument that the number of states needed in a natural dynamic programming algorithm is at most mimsup(H)^k, - lower bounds that show that for almost all graphs H indeed we have c_H ≥ mimsup(H), assuming the (Strong) Exponential-Time Hypothesis, and - an algorithm with running time exp(𝒪(mimsup(H)⋅k log k)) n^𝒪(1). In the last result we do not need to assume that H is a fixed graph. Thus, as a consequence, we obtain that the problem of deciding whether G admits a homomorphism to H is fixed-parameter tractable, when parameterized by cutwidth of G and mimsup(H). The parameter mimsup(H) can be thought of as the p-th root of the maximum induced matching number in the graph obtained by multiplying p copies of H via a certain graph product, where p tends to infinity. It can also be defined as an asymptotic rank parameter of the adjacency matrix of H. Such parameters play a central role in, among others, algebraic complexity theory and additive combinatorics. Our results tightly link the parameterized complexity of a problem to such an asymptotic matrix parameter for the first time.
Cite as

Carla Groenland, Isja Mannens, Jesper Nederlof, Marta Piecyk, and Paweł Rzążewski. Towards Tight Bounds for the Graph Homomorphism Problem Parameterized by Cutwidth via Asymptotic Matrix Parameters. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 77:1-77:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{groenland_et_al:LIPIcs.ICALP.2024.77,
  author =	{Groenland, Carla and Mannens, Isja and Nederlof, Jesper and Piecyk, Marta and Rz\k{a}\.{z}ewski, Pawe{\l}},
  title =	{{Towards Tight Bounds for the Graph Homomorphism Problem Parameterized by Cutwidth via Asymptotic Matrix Parameters}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{77:1--77:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.77},
  URN =		{urn:nbn:de:0030-drops-202208},
  doi =		{10.4230/LIPIcs.ICALP.2024.77},
  annote =	{Keywords: graph homomorphism, cutwidth, asymptotic matrix parameters}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.78
Isomorphism for Tournaments of Small Twin Width

Authors: Martin Grohe and Daniel Neuen

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We prove that isomorphism of tournaments of twin width at most k can be decided in time k^O(log k) n^O(1). This implies that the isomorphism problem for classes of tournaments of bounded or moderately growing twin width is in polynomial time. By comparison, there are classes of undirected graphs of bounded twin width that are isomorphism complete, that is, the isomorphism problem for the classes is as hard as the general graph isomorphism problem. Twin width is a graph parameter that has been introduced only recently (Bonnet et al., FOCS 2020), but has received a lot of attention in structural graph theory since then. On directed graphs, it is functionally smaller than clique width. We prove that on tournaments (but not on general directed graphs) it is also functionally smaller than directed tree width (and thus, the same also holds for cut width and directed path width). Hence, our result implies that tournament isomorphism testing is also fixed-parameter tractable when parameterized by any of these parameters. Our isomorphism algorithm heavily employs group-theoretic techniques. This seems to be necessary: as a second main result, we show that the combinatorial Weisfeiler-Leman algorithm does not decide isomorphism of tournaments of twin width at most 35 if its dimension is o(n). (Throughout this abstract, n is the order of the input graphs.)
Cite as

Martin Grohe and Daniel Neuen. Isomorphism for Tournaments of Small Twin Width. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 78:1-78:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{grohe_et_al:LIPIcs.ICALP.2024.78,
  author =	{Grohe, Martin and Neuen, Daniel},
  title =	{{Isomorphism for Tournaments of Small Twin Width}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{78:1--78:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.78},
  URN =		{urn:nbn:de:0030-drops-202216},
  doi =		{10.4230/LIPIcs.ICALP.2024.78},
  annote =	{Keywords: tournament isomorphism, twin width, fixed-parameter tractability, Weisfeiler-Leman algorithm}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.137
On Classes of Bounded Tree Rank, Their Interpretations, and Efficient Sparsification

Authors: Jakub Gajarský and Rose McCarty

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Graph classes of bounded tree rank were introduced recently in the context of the model checking problem for first-order logic of graphs. These graph classes are a common generalization of graph classes of bounded degree and bounded treedepth, and they are a special case of graph classes of bounded expansion. We introduce a notion of decomposition for these classes and show that these decompositions can be efficiently computed. Also, a natural extension of our decomposition leads to a new characterization and decomposition for graph classes of bounded expansion (and an efficient algorithm computing this decomposition). We then focus on interpretations of graph classes of bounded tree rank. We give a characterization of graph classes interpretable in graph classes of tree rank 2. Importantly, our characterization leads to an efficient sparsification procedure: For any graph class 𝒞 interpretable in a graph class of tree rank at most 2, there is a polynomial time algorithm that to any G ∈ 𝒞 computes a (sparse) graph H from a fixed graph class of tree rank at most 2 such that G = I(H) for a fixed interpretation I. To the best of our knowledge, this is the first efficient "interpretation reversal" result that generalizes the result of Gajarský et al. [LICS 2016], who showed an analogous result for graph classes interpretable in classes of graphs of bounded degree.
Cite as

Jakub Gajarský and Rose McCarty. On Classes of Bounded Tree Rank, Their Interpretations, and Efficient Sparsification. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 137:1-137:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{gajarsky_et_al:LIPIcs.ICALP.2024.137,
  author =	{Gajarsk\'{y}, Jakub and McCarty, Rose},
  title =	{{On Classes of Bounded Tree Rank, Their Interpretations, and Efficient Sparsification}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{137:1--137:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.137},
  URN =		{urn:nbn:de:0030-drops-202802},
  doi =		{10.4230/LIPIcs.ICALP.2024.137},
  annote =	{Keywords: First-order model checking, structural graph theory, structural sparsity}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.146
Solving Promise Equations over Monoids and Groups

Authors: Alberto Larrauri and Stanislav Živný

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We give a complete complexity classification for the problem of finding a solution to a given system of equations over a fixed finite monoid, given that a solution over a more restricted monoid exists. As a corollary, we obtain a complexity classification for the same problem over groups.
Cite as

Alberto Larrauri and Stanislav Živný. Solving Promise Equations over Monoids and Groups. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 146:1-146:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{larrauri_et_al:LIPIcs.ICALP.2024.146,
  author =	{Larrauri, Alberto and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Solving Promise Equations over Monoids and Groups}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{146:1--146:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.146},
  URN =		{urn:nbn:de:0030-drops-202893},
  doi =		{10.4230/LIPIcs.ICALP.2024.146},
  annote =	{Keywords: constraint satisfaction, promise constraint satisfaction, equations, minions}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.150
Homogeneity and Homogenizability: Hard Problems for the Logic SNP

Authors: Jakub Rydval

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
The infinite-domain CSP dichotomy conjecture extends the finite-domain CSP dichotomy theorem to reducts of finitely bounded homogeneous structures. Every countable finitely bounded homogeneous structure is uniquely described by a universal first-order sentence up to isomorphism, and every reduct of such a structure by a sentence of the logic SNP. By Fraïssé’s Theorem, testing the existence of a finitely bounded homogeneous structure for a given universal first-order sentence is equivalent to testing the amalgamation property for the class of its finite models. The present paper motivates a complexity-theoretic view on the classification problem for finitely bounded homogeneous structures. We show that this meta-problem is EXPSPACE-hard or PSPACE-hard, depending on whether the input is specified by a universal sentence or a set of forbidden substructures. By relaxing the input to SNP sentences and the question to the existence of a structure with a finitely bounded homogeneous expansion, we obtain a different meta-problem, closely related to the question of homogenizability. We show that this second meta-problem is already undecidable, even if the input SNP sentence comes from the Datalog fragment and uses at most binary relation symbols. As a byproduct of our proof, we also get the undecidability of some other properties for Datalog programs, e.g., whether they can be rewritten in the logic MMSNP, whether they solve some finite-domain CSP, or whether they define a structure with a homogeneous Ramsey expansion in a finite relational signature.
Cite as

Jakub Rydval. Homogeneity and Homogenizability: Hard Problems for the Logic SNP. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 150:1-150:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{rydval:LIPIcs.ICALP.2024.150,
  author =	{Rydval, Jakub},
  title =	{{Homogeneity and Homogenizability: Hard Problems for the Logic SNP}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{150:1--150:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.150},
  URN =		{urn:nbn:de:0030-drops-202939},
  doi =		{10.4230/LIPIcs.ICALP.2024.150},
  annote =	{Keywords: constraint satisfaction problems, finitely bounded, homogeneous, amalgamation property, universal, SNP, homogenizable}
}
Document
DOI: 10.4230/LIPIcs.CSL.2022.31
Structural Properties of the First-Order Transduction Quasiorder

Authors: Jaroslav Nešetřil, Patrice Ossona de Mendez, and Sebastian Siebertz

Published in: LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)

Abstract
Logical transductions provide a very useful tool to encode classes of structures inside other classes of structures. In this paper we study first-order (FO) transductions and the quasiorder they induce on infinite classes of finite graphs. Surprisingly, this quasiorder is very complex, though shaped by the locality properties of first-order logic. This contrasts with the conjectured simplicity of the monadic second order (MSO) transduction quasiorder. We first establish a local normal form for FO transductions, which is of independent interest. Then we prove that the quotient partial order is a bounded distributive join-semilattice, and that the subposet of additive classes is also a bounded distributive join-semilattice. The FO transduction quasiorder has a great expressive power, and many well studied class properties can be defined using it. We apply these structural properties to prove, among other results, that FO transductions of the class of paths are exactly perturbations of classes with bounded bandwidth, that the local variants of monadic stability and monadic dependence are equivalent to their (standard) non-local versions, and that the classes with pathwidth at most k, for k ≥ 1 form a strict hierarchy in the FO transduction quasiorder.
Cite as

Jaroslav Nešetřil, Patrice Ossona de Mendez, and Sebastian Siebertz. Structural Properties of the First-Order Transduction Quasiorder. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{nesetril_et_al:LIPIcs.CSL.2022.31,
  author =	{Ne\v{s}et\v{r}il, Jaroslav and Ossona de Mendez, Patrice and Siebertz, Sebastian},
  title =	{{Structural Properties of the First-Order Transduction Quasiorder}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{31:1--31:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.31},
  URN =		{urn:nbn:de:0030-drops-157514},
  doi =		{10.4230/LIPIcs.CSL.2022.31},
  annote =	{Keywords: Finite model theory, first-order transductions, structural graph theory}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.ICALP.2018.2
Sparsity - an Algorithmic Perspective (Invited Paper)

Authors: Jaroslav Nesetril

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
It is a well known experience that for sparse structures one can find fast algorithm for some problems which seem to be otherwise complex. The recently developed theory of sparse classes of graphs (and structures) formalizes this. Particularly the dichotomy Nowhere vs Somewhere Dense presents a very robust tool to study and design algorithms and algorithmic metatheorems. This dichotomy can be characterized in many different ways leading tp broad applications. We survey some of the recent highlights. This is a joint work with Patrice Ossona de Mendez (EHESS Paris and Charles University Prague).
Cite as

Jaroslav Nesetril. Sparsity - an Algorithmic Perspective (Invited Paper). In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{nesetril:LIPIcs.ICALP.2018.2,
  author =	{Nesetril, Jaroslav},
  title =	{{Sparsity - an Algorithmic Perspective}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.2},
  URN =		{urn:nbn:de:0030-drops-90062},
  doi =		{10.4230/LIPIcs.ICALP.2018.2},
  annote =	{Keywords: sparse structures, algorithm design}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.126
First-Order Interpretations of Bounded Expansion Classes

Authors: Jakub Gajarský, Stephan Kreutzer, Jaroslav Nesetril, Patrice Ossona de Mendez, Michal Pilipczuk, Sebastian Siebertz, and Szymon Torunczyk

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter tractable over such graph classes. With the aim of generalizing such results to dense graphs, we introduce classes of graphs with structurally bounded expansion, defined as first-order interpretations of classes of bounded expansion. As a first step towards their algorithmic treatment, we provide their characterization analogous to the characterization of classes of bounded expansion via low treedepth decompositions, replacing treedepth by its dense analogue called shrubdepth.
Cite as

Jakub Gajarský, Stephan Kreutzer, Jaroslav Nesetril, Patrice Ossona de Mendez, Michal Pilipczuk, Sebastian Siebertz, and Szymon Torunczyk. First-Order Interpretations of Bounded Expansion Classes. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 126:1-126:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{gajarsky_et_al:LIPIcs.ICALP.2018.126,
  author =	{Gajarsk\'{y}, Jakub and Kreutzer, Stephan and Nesetril, Jaroslav and Ossona de Mendez, Patrice and Pilipczuk, Michal and Siebertz, Sebastian and Torunczyk, Szymon},
  title =	{{First-Order Interpretations of Bounded Expansion Classes}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{126:1--126:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.126},
  URN =		{urn:nbn:de:0030-drops-91300},
  doi =		{10.4230/LIPIcs.ICALP.2018.126},
  annote =	{Keywords: Logical interpretations/transductions, structurally sparse graphs, bounded expansion}
}
Document
DOI: 10.4230/DagSemRep.395
Graph Colorings (Dagstuhl Seminar 03391)

Authors: Jaroslav Nesetril and Gerhard J. Woeginger

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Jaroslav Nesetril and Gerhard J. Woeginger. Graph Colorings (Dagstuhl Seminar 03391). Dagstuhl Seminar Report 395, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2003)

Copy BibTex To Clipboard

@TechReport{nesetril_et_al:DagSemRep.395,
  author =	{Nesetril, Jaroslav and Woeginger, Gerhard J.},
  title =	{{Graph Colorings (Dagstuhl Seminar 03391)}},
  pages =	{1--6},
  ISSN =	{1619-0203},
  year =	{2003},
  type = 	{Dagstuhl Seminar Report},
  number =	{395},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.395},
  URN =		{urn:nbn:de:0030-drops-152757},
  doi =		{10.4230/DagSemRep.395},
}
  • Refine by Author
  • 3 Nesetril, Jaroslav
  • 2 Gajarský, Jakub
  • 2 Ossona de Mendez, Patrice
  • 2 Siebertz, Sebastian
  • 1 Censor-Hillel, Keren
  • Show More...

  • Refine by Classification
  • 4 Theory of computation → Finite Model Theory
  • 3 Mathematics of computing → Graph algorithms
  • 2 Mathematics of computing → Graph theory
  • 2 Theory of computation → Fixed parameter tractability
  • 2 Theory of computation → Logic
  • Show More...

  • Refine by Keyword
  • 2 structural graph theory
  • 1 Approximate cycle counting Fast matrix multiplication
  • 1 Approximate triangle counting
  • 1 Computational Chemistry
  • 1 Fast rectangular matrix multiplication
  • Show More...

  • Refine by Type
  • 12 document

  • Refine by Publication Year
  • 8 2024
  • 2 2018
  • 1 2003
  • 1 2022

© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact