36 Search Results for "Toruńczyk, Szymon"

Document
DOI: 10.4230/LIPIcs.ESA.2024.72
Connectivity Oracles for Predictable Vertex Failures

Authors: Bingbing Hu, Evangelos Kosinas, and Adam Polak

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
The problem of designing connectivity oracles supporting vertex failures is one of the basic data structures problems for undirected graphs. It is already well understood: previous works [Duan-Pettie STOC'10; Long-Saranurak FOCS'22] achieve query time linear in the number of failed vertices, and it is conditionally optimal as long as we require preprocessing time polynomial in the size of the graph and update time polynomial in the number of failed vertices. We revisit this problem in the paradigm of algorithms with predictions: we ask if the query time can be improved if the set of failed vertices can be predicted beforehand up to a small number of errors. More specifically, we design a data structure that, given a graph G = (V,E) and a set of vertices predicted to fail D̂ ⊆ V of size d = |D̂|, preprocesses it in time Õ(d|E|) and then can receive an update given as the symmetric difference between the predicted and the actual set of failed vertices D̂△D = (D̂ ⧵ D) ∪ (D ⧵ D̂) of size η = |D̂△D|, process it in time Õ(η⁴), and after that answer connectivity queries in G ⧵ D in time O(η). Viewed from another perspective, our data structure provides an improvement over the state of the art for the fully dynamic subgraph connectivity problem in the sensitivity setting [Henzinger-Neumann ESA'16]. We argue that the preprocessing time and query time of our data structure are conditionally optimal under standard fine-grained complexity assumptions.
Cite as

Bingbing Hu, Evangelos Kosinas, and Adam Polak. Connectivity Oracles for Predictable Vertex Failures. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 72:1-72:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hu_et_al:LIPIcs.ESA.2024.72,
  author =	{Hu, Bingbing and Kosinas, Evangelos and Polak, Adam},
  title =	{{Connectivity Oracles for Predictable Vertex Failures}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{72:1--72:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.72},
  URN =		{urn:nbn:de:0030-drops-211437},
  doi =		{10.4230/LIPIcs.ESA.2024.72},
  annote =	{Keywords: Data structures, graph connectivity, algorithms with predictions}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.29
Strategic Dominance: A New Preorder for Nondeterministic Processes

Authors: Thomas A. Henzinger, Nicolas Mazzocchi, and N. Ege Saraç

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
We study the following refinement relation between nondeterministic state-transition models: model ℬ strategically dominates model 𝒜 iff every deterministic refinement of 𝒜 is language contained in some deterministic refinement of ℬ. While language containment is trace inclusion, and the (fair) simulation preorder coincides with tree inclusion, strategic dominance falls strictly between the two and can be characterized as "strategy inclusion" between 𝒜 and ℬ: every strategy that resolves the nondeterminism of 𝒜 is dominated by a strategy that resolves the nondeterminism of ℬ. Strategic dominance can be checked in 2-ExpTime by a decidable first-order Presburger logic with quantification over words and strategies, called resolver logic. We give several other applications of resolver logic, including checking the co-safety, co-liveness, and history-determinism of boolean and quantitative automata, and checking the inclusion between hyperproperties that are specified by nondeterministic boolean and quantitative automata.
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Thomas A. Henzinger, Nicolas Mazzocchi, and N. Ege Saraç. Strategic Dominance: A New Preorder for Nondeterministic Processes. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{henzinger_et_al:LIPIcs.CONCUR.2024.29,
  author =	{Henzinger, Thomas A. and Mazzocchi, Nicolas and Sara\c{c}, N. Ege},
  title =	{{Strategic Dominance: A New Preorder for Nondeterministic Processes}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{29:1--29:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.29},
  URN =		{urn:nbn:de:0030-drops-208011},
  doi =		{10.4230/LIPIcs.CONCUR.2024.29},
  annote =	{Keywords: quantitative automata, refinement relation, resolver, strategy, history-determinism}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.31
Bi-Reachability in Petri Nets with Data

Authors: Łukasz Kamiński and Sławomir Lasota

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
We investigate Petri nets with data, an extension of plain Petri nets where tokens carry values from an infinite data domain, and executability of transitions is conditioned by equalities between data values. We provide a decision procedure for the bi-reachability problem: given a Petri net and its two configurations, we ask if each of the configurations is reachable from the other. This pushes forward the decidability borderline, as the bi-reachability problem subsumes the coverability problem (which is known to be decidable) and is subsumed by the reachability problem (whose decidability status is unknown).
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Łukasz Kamiński and Sławomir Lasota. Bi-Reachability in Petri Nets with Data. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 31:1-31:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kaminski_et_al:LIPIcs.CONCUR.2024.31,
  author =	{Kami\'{n}ski, {\L}ukasz and Lasota, S{\l}awomir},
  title =	{{Bi-Reachability in Petri Nets with Data}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{31:1--31:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.31},
  URN =		{urn:nbn:de:0030-drops-208038},
  doi =		{10.4230/LIPIcs.CONCUR.2024.31},
  annote =	{Keywords: Petri nets, Petri nets with data, reachability, bi-reachability, reversible reachability, mutual reachability, orbit-finite sets}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.35
Nominal Tree Automata with Name Allocation

Authors: Simon Prucker and Lutz Schröder

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
Data trees serve as an abstraction of structured data, such as XML documents. A number of specification formalisms for languages of data trees have been developed, many of them adhering to the paradigm of register automata, which is based on storing data values encountered on the tree in registers for subsequent comparison with further data values. Already on word languages, the expressiveness of such automata models typically increases with the power of control (e.g. deterministic, non-deterministic, alternating). Language inclusion is typically undecidable for non-deterministic or alternating models unless the number of registers is radically restricted, and even then often remains non-elementary. We present an automaton model for data trees that retains a reasonable level of expressiveness, in particular allows non-determinism and any number of registers, while admitting language inclusion checking in elementary complexity, in fact in parametrized exponential time. We phrase the description of our automaton model in the language of nominal sets, building on the recently introduced paradigm of explicit name allocation in nominal automata.
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Simon Prucker and Lutz Schröder. Nominal Tree Automata with Name Allocation. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 35:1-35:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{prucker_et_al:LIPIcs.CONCUR.2024.35,
  author =	{Prucker, Simon and Schr\"{o}der, Lutz},
  title =	{{Nominal Tree Automata with Name Allocation}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{35:1--35:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.35},
  URN =		{urn:nbn:de:0030-drops-208071},
  doi =		{10.4230/LIPIcs.CONCUR.2024.35},
  annote =	{Keywords: Data languages, tree automata, nominal automata, inclusion checking}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.32
Symmetric-Difference (Degeneracy) and Signed Tree Models

Authors: Édouard Bonnet, Julien Duron, John Sylvester, and Viktor Zamaraev

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
We introduce a dense counterpart of graph degeneracy, which extends the recently-proposed invariant symmetric difference. We say that a graph has sd-degeneracy (for symmetric-difference degeneracy) at most d if it admits an elimination order of its vertices where a vertex u can be removed whenever it has a d-twin, i.e., another vertex v such that at most d vertices outside {u,v} are neighbors of exactly one of u, v. The family of graph classes of bounded sd-degeneracy is a superset of that of graph classes of bounded degeneracy or of bounded flip-width, and more generally, of bounded symmetric difference. Unlike most graph parameters, sd-degeneracy is not hereditary: it may be strictly smaller on a graph than on some of its induced subgraphs. In particular, every n-vertex graph is an induced subgraph of some O(n²)-vertex graph of sd-degeneracy 1. In spite of this and the breadth of classes of bounded sd-degeneracy, we devise Õ(√n)-bit adjacency labeling schemes for them, which are optimal up to the hidden polylogarithmic factor. This is attained on some even more general classes, consisting of graphs G whose vertices bijectively map to the leaves of a tree T, where transversal edges and anti-edges added to T define the edge set of G. We call such graph representations signed tree models as they extend the so-called tree models (or twin-decompositions) developed in the context of twin-width, by adding transversal anti-edges. While computing the degeneracy of a graph takes linear time, we show that determining its symmetric difference is para-co-NP-complete. This may seem surprising as symmetric difference can serve as a short-sighted first approximation of twin-width, whose computation is para-NP-complete. Indeed, we show that deciding if the symmetric difference of an input graph is at most 8 is co-NP-complete. We also show that deciding if the sd-degeneracy is at most 6 is NP-complete, contrasting with the symmetric difference.
Cite as

Édouard Bonnet, Julien Duron, John Sylvester, and Viktor Zamaraev. Symmetric-Difference (Degeneracy) and Signed Tree Models. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bonnet_et_al:LIPIcs.MFCS.2024.32,
  author =	{Bonnet, \'{E}douard and Duron, Julien and Sylvester, John and Zamaraev, Viktor},
  title =	{{Symmetric-Difference (Degeneracy) and Signed Tree Models}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{32:1--32:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.32},
  URN =		{urn:nbn:de:0030-drops-205886},
  doi =		{10.4230/LIPIcs.MFCS.2024.32},
  annote =	{Keywords: symmetric difference, degeneracy, adjacency labeling schemes, NP-hardness}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.47
Preservation Theorems on Sparse Classes Revisited

Authors: Anuj Dawar and Ioannis Eleftheriadis

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
We revisit the work studying homomorphism preservation for first-order logic in sparse classes of structures initiated in [Atserias et al., JACM 2006] and [Dawar, JCSS 2010]. These established that first-order logic has the homomorphism preservation property in any sparse class that is monotone and addable. It turns out that the assumption of addability is not strong enough for the proofs given. We demonstrate this by constructing classes of graphs of bounded treewidth which are monotone and addable but fail to have homomorphism preservation. We also show that homomorphism preservation fails on the class of planar graphs. On the other hand, the proofs of homomorphism preservation can be recovered by replacing addability by a stronger condition of amalgamation over bottlenecks. This is analogous to a similar condition formulated for extension preservation in [Atserias et al., SiCOMP 2008].
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Anuj Dawar and Ioannis Eleftheriadis. Preservation Theorems on Sparse Classes Revisited. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 47:1-47:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dawar_et_al:LIPIcs.MFCS.2024.47,
  author =	{Dawar, Anuj and Eleftheriadis, Ioannis},
  title =	{{Preservation Theorems on Sparse Classes Revisited}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{47:1--47:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.47},
  URN =		{urn:nbn:de:0030-drops-206036},
  doi =		{10.4230/LIPIcs.MFCS.2024.47},
  annote =	{Keywords: Homomorphism preservation, sparsity, finite model theory, planar graphs}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.61
ℋ-Clique-Width and a Hereditary Analogue of Product Structure

Authors: Petr Hliněný and Jan Jedelský

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
We introduce a novel generalization of the notion of clique-width which aims to bridge the gap between classical hereditary width measures and the recently introduced graph product structure theory. Bounding the new H-clique-width, in the special case of H being the class of paths, is equivalent to admitting a hereditary (i.e., induced) product structure of a path times a graph of bounded clique-width. Furthermore, every graph admitting the usual (non-induced) product structure of a path times a graph of bounded tree-width, has bounded H-clique-width and, as a consequence, it admits the usual product structure in an induced way. We prove further basic properties of H-clique-width in general.
Cite as

Petr Hliněný and Jan Jedelský. ℋ-Clique-Width and a Hereditary Analogue of Product Structure. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 61:1-61:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hlineny_et_al:LIPIcs.MFCS.2024.61,
  author =	{Hlin\v{e}n\'{y}, Petr and Jedelsk\'{y}, Jan},
  title =	{{ℋ-Clique-Width and a Hereditary Analogue of Product Structure}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{61:1--61:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.61},
  URN =		{urn:nbn:de:0030-drops-206176},
  doi =		{10.4230/LIPIcs.MFCS.2024.61},
  annote =	{Keywords: product structure, hereditary class, clique-width, twin-width}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.66
Twin-Width of Graphs on Surfaces

Authors: Daniel Kráľ, Kristýna Pekárková, and Kenny Štorgel

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
Twin-width is a width parameter introduced by Bonnet, Kim, Thomassé and Watrigant [FOCS'20, JACM'22], which has many structural and algorithmic applications. Hliněný and Jedelský [ICALP'23] showed that every planar graph has twin-width at most 8. We prove that the twin-width of every graph embeddable in a surface of Euler genus g is at most 18√{47g} + O(1), which is asymptotically best possible as it asymptotically differs from the lower bound by a constant multiplicative factor. Our proof also yields a quadratic time algorithm to find a corresponding contraction sequence. To prove the upper bound on twin-width of graphs embeddable in surfaces, we provide a stronger version of the Product Structure Theorem for graphs of Euler genus g that asserts that every such graph is a subgraph of the strong product of a path and a graph with a tree-decomposition with all bags of size at most eight with a single exceptional bag of size max{6, 32g-37}.
Cite as

Daniel Kráľ, Kristýna Pekárková, and Kenny Štorgel. Twin-Width of Graphs on Surfaces. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 66:1-66:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kral_et_al:LIPIcs.MFCS.2024.66,
  author =	{Kr\'{a}\v{l}, Daniel and Pek\'{a}rkov\'{a}, Krist\'{y}na and \v{S}torgel, Kenny},
  title =	{{Twin-Width of Graphs on Surfaces}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{66:1--66:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.66},
  URN =		{urn:nbn:de:0030-drops-206226},
  doi =		{10.4230/LIPIcs.MFCS.2024.66},
  annote =	{Keywords: twin-width, graphs on surfaces, fixed parameter tractability}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.53
Parameterized Algorithms for Coordinated Motion Planning: Minimizing Energy

Authors: Argyrios Deligkas, Eduard Eiben, Robert Ganian, Iyad Kanj, and M. S. Ramanujan

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

Abstract
We study the parameterized complexity of a generalization of the coordinated motion planning problem on graphs, where the goal is to route a specified subset of a given set of k robots to their destinations with the aim of minimizing the total energy (i.e., the total length traveled). We develop novel techniques to push beyond previously-established results that were restricted to solid grids. We design a fixed-parameter additive approximation algorithm for this problem parameterized by k alone. This result, which is of independent interest, allows us to prove the following two results pertaining to well-studied coordinated motion planning problems: (1) A fixed-parameter algorithm, parameterized by k, for routing a single robot to its destination while avoiding the other robots, which is related to the famous Rush-Hour Puzzle; and (2) a fixed-parameter algorithm, parameterized by k plus the treewidth of the input graph, for the standard Coordinated Motion Planning (CMP) problem in which we need to route all the k robots to their destinations. The latter of these results implies, among others, the fixed-parameter tractability of CMP parameterized by k on graphs of bounded outerplanarity, which include bounded-height subgrids. We complement the above results with a lower bound which rules out the fixed-parameter tractability for CMP when parameterized by the total energy. This contrasts the recently-obtained tractability of the problem on solid grids under the same parameterization. As our final result, we strengthen the aforementioned fixed-parameter tractability to hold not only on solid grids but all graphs of bounded local treewidth - a class including, among others, all graphs of bounded genus.
Cite as

Argyrios Deligkas, Eduard Eiben, Robert Ganian, Iyad Kanj, and M. S. Ramanujan. Parameterized Algorithms for Coordinated Motion Planning: Minimizing Energy. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 53:1-53:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{deligkas_et_al:LIPIcs.ICALP.2024.53,
  author =	{Deligkas, Argyrios and Eiben, Eduard and Ganian, Robert and Kanj, Iyad and Ramanujan, M. S.},
  title =	{{Parameterized Algorithms for Coordinated Motion Planning: Minimizing Energy}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{53:1--53:18},
  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.2024.53},
  URN =		{urn:nbn:de:0030-drops-201968},
  doi =		{10.4230/LIPIcs.ICALP.2024.53},
  annote =	{Keywords: coordinated motion planning, multi-agent path finding, parameterized complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.33
Kernelization Dichotomies for Hitting Subgraphs Under Structural Parameterizations

Authors: Marin Bougeret, Bart M. P. Jansen, and Ignasi Sau

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

Abstract
For a fixed graph H, the H-Subgraph Hitting problem consists in deleting the minimum number of vertices from an input graph to obtain a graph without any occurrence of H as a subgraph. This problem can be seen as a generalization of Vertex Cover, which corresponds to the case H = K₂. We initiate a study of H-Subgraph Hitting from the point of view of characterizing structural parameterizations that allow for polynomial kernels, within the recently active framework of taking as the parameter the number of vertex deletions to obtain a graph in a "simple" class 𝒞. Our main contribution is to identify graph parameters that, when H-Subgraph Hitting is parameterized by the vertex-deletion distance to a class 𝒞 where any of these parameters is bounded, and assuming standard complexity assumptions and that H is biconnected, allow us to prove the following sharp dichotomy: the problem admits a polynomial kernel if and only if H is a clique. These new graph parameters are inspired by the notion of 𝒞-elimination distance introduced by Bulian and Dawar [Algorithmica 2016], and generalize it in two directions. Our results also apply to the version of the problem where one wants to hit H as an induced subgraph, and imply in particular, that the problems of hitting minors and hitting (induced) subgraphs have a substantially different behavior with respect to the existence of polynomial kernels under structural parameterizations.
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Marin Bougeret, Bart M. P. Jansen, and Ignasi Sau. Kernelization Dichotomies for Hitting Subgraphs Under Structural Parameterizations. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 33:1-33:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bougeret_et_al:LIPIcs.ICALP.2024.33,
  author =	{Bougeret, Marin and Jansen, Bart M. P. and Sau, Ignasi},
  title =	{{Kernelization Dichotomies for Hitting Subgraphs Under Structural Parameterizations}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{33:1--33:20},
  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.2024.33},
  URN =		{urn:nbn:de:0030-drops-201766},
  doi =		{10.4230/LIPIcs.ICALP.2024.33},
  annote =	{Keywords: hitting subgraphs, hitting induced subgraphs, parameterized complexity, polynomial kernel, complexity dichotomy, elimination distance}
}
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)

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@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 A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.109
Better Decremental and Fully Dynamic Sensitivity Oracles for Subgraph Connectivity

Authors: Yaowei Long and Yunfan Wang

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

Abstract
We study the sensitivity oracles problem for subgraph connectivity in the decremental and fully dynamic settings. In the fully dynamic setting, we preprocess an n-vertices m-edges undirected graph G with n_{off} deactivated vertices initially and the others are activated. Then we receive a single update D ⊆ V(G) of size |D| = d ≤ d_{⋆}, representing vertices whose states will be switched. Finally, we get a sequence of queries, each of which asks the connectivity of two given vertices u and v in the activated subgraph. The decremental setting is a special case when there is no deactivated vertex initially, and it is also known as the vertex-failure connectivity oracles problem. We present a better deterministic vertex-failure connectivity oracle with Ô(d_{⋆}m) preprocessing time, Õ(m) space, Õ(d²) update time and O(d) query time, which improves the update time of the previous almost-optimal oracle [Long and Saranurak, 2022] from Ô(d²) to Õ(d²). We also present a better deterministic fully dynamic sensitivity oracle for subgraph connectivity with Ô(min{m(n_{off} + d_{⋆}),n^{ω}}) preprocessing time, Õ(min{m(n_{off} + d_{⋆}),n²}) space, Õ(d²) update time and O(d) query time, which significantly improves the update time of the state of the art [Bingbing Hu et al., 2023] from Õ(d⁴) to Õ(d²). Furthermore, our solution is even almost-optimal assuming popular fine-grained complexity conjectures.
Cite as

Yaowei Long and Yunfan Wang. Better Decremental and Fully Dynamic Sensitivity Oracles for Subgraph Connectivity. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 109:1-109:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{long_et_al:LIPIcs.ICALP.2024.109,
  author =	{Long, Yaowei and Wang, Yunfan},
  title =	{{Better Decremental and Fully Dynamic Sensitivity Oracles for Subgraph Connectivity}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{109:1--109:20},
  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.2024.109},
  URN =		{urn:nbn:de:0030-drops-202523},
  doi =		{10.4230/LIPIcs.ICALP.2024.109},
  annote =	{Keywords: connectivity, sensitivity}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.125
Edit Distance of Finite State Transducers

Authors: C. Aiswarya, Amaldev Manuel, and Saina Sunny

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

Abstract
We lift metrics over words to metrics over word-to-word transductions, by defining the distance between two transductions as the supremum of the distances of their respective outputs over all inputs. This allows to compare transducers beyond equivalence. Two transducers are close (resp. k-close) with respect to a metric if their distance is finite (resp. at most k). Over integer-valued metrics computing the distance between transducers is equivalent to deciding the closeness and k-closeness problems. For common integer-valued edit distances such as, Hamming, transposition, conjugacy and Levenshtein family of distances, we show that the closeness and the k-closeness problems are decidable for functional transducers. Hence, the distance with respect to these metrics is also computable. Finally, we relate the notion of distance between functions to the notions of diameter of a relation and index of a relation in another. We show that computing edit distance between functional transducers is equivalent to computing diameter of a rational relation and both are a specific instance of the index problem of rational relations.
Cite as

C. Aiswarya, Amaldev Manuel, and Saina Sunny. Edit Distance of Finite State Transducers. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 125:1-125:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{aiswarya_et_al:LIPIcs.ICALP.2024.125,
  author =	{Aiswarya, C. and Manuel, Amaldev and Sunny, Saina},
  title =	{{Edit Distance of Finite State Transducers}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{125:1--125:20},
  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.2024.125},
  URN =		{urn:nbn:de:0030-drops-202682},
  doi =		{10.4230/LIPIcs.ICALP.2024.125},
  annote =	{Keywords: transducers, edit distance, conjugacy}
}
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)

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@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.2024.150
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)

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@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}
}
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