19 Search Results for "Bonsma, Paul"

Document
DOI: 10.4230/LIPIcs.STACS.2026.19
A Linear Kernel for Independent Set Reconfiguration in Planar Graphs

Authors: Nicolas Bousquet and Daniel W. Cranston

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Fix a positive integer r, and a graph G that is K_{3,r}-minor-free. Let I_s and I_t be two independent sets in G, each of size k. We begin with a "token" on each vertex of I_s and seek to move all tokens to I_t, by repeated "token jumping", removing a single token from one vertex and placing it on another vertex. We require that each intermediate arrangement of tokens again specifies an independent set of size k. Given G, I_s, and I_t, we ask whether there exists a sequence of token jumps that transforms I_s into I_t. When k is part of the input, this problem is known to be PSPACE-complete. But it was shown by Ito, Kamiński, and Ono [Ito et al., 2014] to be fixed-parameter tractable. That is, the problem can be solved in time f(k)⋅ P(n), for some function f and polynomial P, where n denotes the order of G. Here we strengthen the upper bound on the running time in terms of k by showing that the problem has a kernel of size linear in k. More precisely, we transform an arbitrary input problem on a K_{3,r}-minor-free graph (for some fixed positive integer r) into an equivalent problem on a (K_{3,r}-minor-free) graph with order O(k). This answers positively a question of Bousquet, Mouawad, Nishimura, and Siebertz [Nicolas Bousquet et al., 2022] and improves the recent quadratic kernel of Cranston, Mühlenthaler, and Peyrille [Daniel W. Cranston et al., 2024]. For planar graphs, we further strengthen this upper bound to get a kernel of size at most 42k.
Cite as

Nicolas Bousquet and Daniel W. Cranston. A Linear Kernel for Independent Set Reconfiguration in Planar Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bousquet_et_al:LIPIcs.STACS.2026.19,
  author =	{Bousquet, Nicolas and Cranston, Daniel W.},
  title =	{{A Linear Kernel for Independent Set Reconfiguration in Planar Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{19:1--19:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.19},
  URN =		{urn:nbn:de:0030-drops-255081},
  doi =		{10.4230/LIPIcs.STACS.2026.19},
  annote =	{Keywords: Reconfiguration, Independent Set, Kernel, Planar graphs}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.25
Exact Algorithms and Hardness Result for the Boolean Connectivity Problem of k-Horn Formulas

Authors: Takashi Horiyama, Yuto Okura, Kazuhisa Seto, and Junichi Teruyama

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
The Boolean connectivity problem asks whether the set of satisfying assignments of a given Boolean formula forms a connected subgraph in the n-dimensional hypercube. This problem is known to be coNP-complete, even when restricted to k-Horn formulas for k ≥ 3, as shown by Makino, Tamaki, and Yamamoto. In this paper, we further investigate the complexity of the Boolean connectivity problem for k-Horn formulas, referred to as Conn k-Horn. We first present an exact exponential-time algorithm for Conn k-Horn without any structural restrictions. Our algorithm builds on the deterministic PPZ algorithm proposed by Paturi, Pudlák, and Zane. It runs in O^*(2^{(1-1/2k)n}) time, achieving an exponential improvement over the previously known algorithm for the Boolean connectivity problem of k-CNF formulas, shown by Makino, Tamaki, and Yamamoto. We then examine both algorithmic and hardness results for Conn 3-Horn under bounded variable occurrences. On the algorithmic side, we propose a polynomial-time algorithm for Conn 3-Horn when each clause contains exactly three literals and each variable appears at most three times. This result generalizes to Conn k-Horn under the same structural constraints, in which each clause contains exactly k literals and each variable appears at most k times. On the hardness side, we prove that Conn 3-Horn remains coNP-complete even when restricted to instances in which each variable appears exactly four times.
Cite as

Takashi Horiyama, Yuto Okura, Kazuhisa Seto, and Junichi Teruyama. Exact Algorithms and Hardness Result for the Boolean Connectivity Problem of k-Horn Formulas. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 25:1-25:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{horiyama_et_al:LIPIcs.IPEC.2025.25,
  author =	{Horiyama, Takashi and Okura, Yuto and Seto, Kazuhisa and Teruyama, Junichi},
  title =	{{Exact Algorithms and Hardness Result for the Boolean Connectivity Problem of k-Horn Formulas}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{25:1--25:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.25},
  URN =		{urn:nbn:de:0030-drops-251577},
  doi =		{10.4230/LIPIcs.IPEC.2025.25},
  annote =	{Keywords: k-Horn, Boolean connectivity, bounded variable occurrence, hardness, exact algorithm, satisfiability}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.31
Token Sliding Independent Set Reconfiguration on Block Graphs

Authors: Mathew C. Francis and Veena Prabhakaran

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
Let S be an independent set of a simple undirected graph G. Suppose that each vertex of S has a token placed on it. The tokens are allowed to be moved, one at a time, by sliding along the edges of G while maintaining the property that after each move, the vertices having tokens always form an independent set of G. We would like to determine whether the tokens can be eventually brought to stay on the vertices of another independent set S' of G in this manner. In other words, we would like to decide if we can transform S into S' through a sequence of steps, each of which involves substituting a vertex in the current independent set with one of its neighbours to obtain another independent set. This problem of determining if one independent set of a graph "is reachable" from another independent set of it is known to be PSPACE-hard even for split graphs, planar graphs, and graphs of bounded treewidth. Polynomial time algorithms have been obtained for certain graph classes like trees, interval graphs, claw-free graphs, and bipartite permutation graphs. We present a polynomial time algorithm for the problem on block graphs, which are the graphs in which every maximal 2-connected subgraph is a clique. Our algorithm is the first generalization of the known polynomial time algorithm for trees to a larger class of graphs.
Cite as

Mathew C. Francis and Veena Prabhakaran. Token Sliding Independent Set Reconfiguration on Block Graphs. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{francis_et_al:LIPIcs.FSTTCS.2025.31,
  author =	{Francis, Mathew C. and Prabhakaran, Veena},
  title =	{{Token Sliding Independent Set Reconfiguration on Block Graphs}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{31:1--31:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.31},
  URN =		{urn:nbn:de:0030-drops-251120},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.31},
  annote =	{Keywords: Token sliding independent set reconfiguration, block graphs, polynomial time algorithm}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.39
Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules

Authors: Shuichi Hirahara, Naoto Ohsaka, Tatsuhiro Suga, Akira Suzuki, Yuma Tamura, and Xiao Zhou

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
In reconfiguration problems, we are given two feasible solutions to a graph problem and asked whether one can be transformed into the other via a sequence of feasible intermediate solutions under a given reconfiguration rule. While earlier work focused on modifying a single element at a time, recent studies have started examining how different rules impact computational complexity. Motivated by recent progress, we study Independent Set Reconfiguration (ISR) and Vertex Cover Reconfiguration (VCR) under the k-Token Jumping (k-TJ) and k-Token Sliding (k-TS) models. In k-TJ, up to k vertices may be replaced, while k-TS additionally requires a perfect matching between removed and added vertices. It is known that the complexity of ISR crucially depends on k, ranging from PSPACE-complete and NP-complete to polynomial-time solvable. In this paper, we further explore the gradient of computational complexity of the problems. We first show that ISR under k-TJ with k = |I| - μ remains NP-hard when μ is any fixed positive integer and the input graph is restricted to graphs of maximum degree 3 or planar graphs of maximum degree 4, where |I| is the size of feasible solutions. In addition, we prove that the problem belongs to NP not only for μ = O(1) but also for μ = O(log |I|). In contrast, we show that VCR under k-TJ is in XP when parameterized by μ = |S| - k, where |S| is the size of feasible solutions. Furthermore, we establish the PSPACE-completeness of ISR and VCR under both k-TJ and k-TS on several graph classes, for fixed k as well as superconstant k relative to the size of feasible solutions.
Cite as

Shuichi Hirahara, Naoto Ohsaka, Tatsuhiro Suga, Akira Suzuki, Yuma Tamura, and Xiao Zhou. Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hirahara_et_al:LIPIcs.ISAAC.2025.39,
  author =	{Hirahara, Shuichi and Ohsaka, Naoto and Suga, Tatsuhiro and Suzuki, Akira and Tamura, Yuma and Zhou, Xiao},
  title =	{{Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{39:1--39:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.39},
  URN =		{urn:nbn:de:0030-drops-249474},
  doi =		{10.4230/LIPIcs.ISAAC.2025.39},
  annote =	{Keywords: combinatorial reconfiguration, extended reconfiguration rule, independent set reconfiguration, vertex cover reconfiguration, PSPACE-completeness, NP-completeness}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.33
Coloring Reconfiguration Under Color Swapping

Authors: Janosch Fuchs, Rin Saito, Tatsuhiro Suga, Takahiro Suzuki, and Yuma Tamura

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
In the Coloring Reconfiguration problem, we are given two proper k-colorings of a graph and asked to decide whether one can be transformed into the other by repeatedly applying a specified recoloring rule, while maintaining a proper coloring throughout. For this problem, two recoloring rules have been widely studied: single-vertex recoloring and Kempe chain recoloring. In this paper, we introduce a new rule, called color swapping, where two adjacent vertices may exchange their colors, so that the resulting coloring remains proper, and study the computational complexity of the problem under this rule. We first establish a complexity dichotomy with respect to k: the problem is solvable in polynomial time for k ≤ 2, and is PSPACE-complete for k ≥ 3. We further show that the problem remains PSPACE-complete even on restricted graph classes, including bipartite graphs, split graphs, and planar graphs of bounded degree. In contrast, we present polynomial-time algorithms for several graph classes: for paths when k = 3, for split graphs when k is fixed, and for cographs when k is arbitrary.
Cite as

Janosch Fuchs, Rin Saito, Tatsuhiro Suga, Takahiro Suzuki, and Yuma Tamura. Coloring Reconfiguration Under Color Swapping. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fuchs_et_al:LIPIcs.ISAAC.2025.33,
  author =	{Fuchs, Janosch and Saito, Rin and Suga, Tatsuhiro and Suzuki, Takahiro and Tamura, Yuma},
  title =	{{Coloring Reconfiguration Under Color Swapping}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{33:1--33:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.33},
  URN =		{urn:nbn:de:0030-drops-249411},
  doi =		{10.4230/LIPIcs.ISAAC.2025.33},
  annote =	{Keywords: Combinatorial reconfiguration, graph coloring, PSPACE-complete, graph algorithm}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.4
Finding d-Cuts in Claw-Free Graphs

Authors: Jungho Ahn, Tala Eagling-Vose, Felicia Lucke, Daniël Paulusma, and Siani Smith

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
The Matching Cut problem is to decide if the vertex set of a connected graph can be partitioned into two non-empty sets B and R such that the edges between B and R form a matching, that is, every vertex in B has at most one neighbour in R, and vice versa. If for some integer d ≥ 1, we allow every vertex in B to have at most d neighbours in R, and vice versa, we obtain the more general problem d-Cut. It is known that d-Cut is NP-complete for every d ≥ 1. However, for claw-free graphs, it is only known that d-Cut is polynomial-time solvable for d = 1 and NP-complete for d ≥ 3. We resolve the missing case d = 2 by proving NP-completeness. This follows from our more general study, in which we also bound the maximum degree. That is, we prove that for every d ≥ 2, d-Cut, restricted to claw-free graphs of maximum degree p, is constant-time solvable if p ≤ 2d+1 and NP-complete if p ≥ 2d+3. Moreover, in the former case, we can find a d-cut in linear time. We also show how our positive results for claw-free graphs can be generalized to S_{1^t,𝓁}-free graphs where S_{1^t,𝓁} is the graph obtained from a star on t+2 vertices by subdividing one of its edges exactly 𝓁 times.
Cite as

Jungho Ahn, Tala Eagling-Vose, Felicia Lucke, Daniël Paulusma, and Siani Smith. Finding d-Cuts in Claw-Free Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ahn_et_al:LIPIcs.ISAAC.2025.4,
  author =	{Ahn, Jungho and Eagling-Vose, Tala and Lucke, Felicia and Paulusma, Dani\"{e}l and Smith, Siani},
  title =	{{Finding d-Cuts in Claw-Free Graphs}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.4},
  URN =		{urn:nbn:de:0030-drops-249121},
  doi =		{10.4230/LIPIcs.ISAAC.2025.4},
  annote =	{Keywords: matching cut, d-cut, claw-free, maximum degree}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.11
Finding Diverse Solutions in Combinatorial Problems with a Distributive Lattice Structure

Authors: Mark de Berg, Andrés López Martínez, and Frits Spieksma

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
We generalize the polynomial-time solvability of k-Diverse Minimum s-t Cuts (De Berg et al., ISAAC'23) to a wider class of combinatorial problems whose solution sets have a distributive lattice structure. We identify three structural conditions that, when met by a problem, ensure that a k-sized multiset of maximally-diverse solutions - measured by the sum of pairwise Hamming distances - can be found in polynomial time. We apply this framework to obtain polynomial-time algorithms for finding diverse minimum s-t cuts, diverse stable matchings, and diverse market-clearing price vectors. Moreover, we show that the framework extends to two other natural measures of diversity. Lastly, we present a simpler algorithmic framework for finding a largest set of pairwise disjoint solutions in problems that meet these structural conditions.
Cite as

Mark de Berg, Andrés López Martínez, and Frits Spieksma. Finding Diverse Solutions in Combinatorial Problems with a Distributive Lattice Structure. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{deberg_et_al:LIPIcs.ISAAC.2025.11,
  author =	{de Berg, Mark and L\'{o}pez Mart{\'\i}nez, Andr\'{e}s and Spieksma, Frits},
  title =	{{Finding Diverse Solutions in Combinatorial Problems with a Distributive Lattice Structure}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{11:1--11:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.11},
  URN =		{urn:nbn:de:0030-drops-249197},
  doi =		{10.4230/LIPIcs.ISAAC.2025.11},
  annote =	{Keywords: Diversity, Lattice Theory, Submodular Function Minimization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.110
Faster Exponential Algorithms for Cut Problems via Geometric Data Structures

Authors: László Kozma and Junqi Tan

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
For many hard computational problems, simple algorithms that run in time 2ⁿ ⋅ n^O(1) arise, say, from enumerating all subsets of a size-n set. Finding (exponentially) faster algorithms is a natural goal that has driven much of the field of exact exponential algorithms (e.g., see Fomin and Kratsch, 2010). In this paper we obtain algorithms with running time O(1.9999977ⁿ) on input graphs with n vertices, for the following well-studied problems: - d-Cut: find a proper cut in which no vertex has more than d neighbors on the other side of the cut; - Internal Partition: find a proper cut in which every vertex has at least as many neighbors on its side of the cut as on the other side; and - (α,β)-Domination: given intervals α,β ⊆ [0,n], find a subset S of the vertices, so that for every vertex v ∈ S the number of neighbors of v in S is from α and for every vertex v ∉ S, the number of neighbors of v in S is from β. Our algorithms are exceedingly simple, combining the split and list technique (Horowitz and Sahni, 1974; Williams, 2005) with a tool from computational geometry: orthogonal range searching in the moderate dimensional regime (Chan, 2017). Our technique is applicable to the decision, optimization and counting versions of these problems and easily extends to various generalizations with more fine-grained, vertex-specific constraints, as well as to directed, balanced, and other variants. Algorithms with running times of the form cⁿ, for c < 2, were known for the first problem only for constant d, and for the third problem for certain special cases of α and β; for the second problem we are not aware of such results.
Cite as

László Kozma and Junqi Tan. Faster Exponential Algorithms for Cut Problems via Geometric Data Structures. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 110:1-110:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kozma_et_al:LIPIcs.ESA.2025.110,
  author =	{Kozma, L\'{a}szl\'{o} and Tan, Junqi},
  title =	{{Faster Exponential Algorithms for Cut Problems via Geometric Data Structures}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{110:1--110:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.110},
  URN =		{urn:nbn:de:0030-drops-245796},
  doi =		{10.4230/LIPIcs.ESA.2025.110},
  annote =	{Keywords: graph algorithms, cuts, exponential time, data structures}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.43
On the Complexity of Finding 1-Center Spanning Trees

Authors: Pin-Hsian Lee, Meng-Tsung Tsai, and Hung-Lung Wang

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We consider the problem of finding a spanning tree T of a given undirected graph G such that any other spanning tree can be obtained from T by removing k edges and subsequently adding k edges, where k is minimized over all spanning trees of G. We refer to this minimum k as the treeradius of G. Treeradius is an interesting graph parameter with natural interpretations: (1) It is the smallest radius of a Hamming ball centered at an extreme point of the spanning tree polytope that covers the entire polytope. (2) Any graph with bounded treeradius also has bounded treewidth. Consequently, if a problem admits a fixed-parameter algorithm parameterized by treewidth, it also admits a fixed-parameter algorithm parameterized by treeradius. In this paper, we show that computing the exact treeradius for n-vertex graphs requires 2^Ω(n) time under the Exponential Time Hypothesis (ETH) and does not admit a PTAS, with an inapproximability bound of 1153/1152, unless P = NP. This hardness result is surprising, as treeradius has significantly higher ETH complexity compared to analogous problems on shortest path polytopes and star subgraph polytopes.
Cite as

Pin-Hsian Lee, Meng-Tsung Tsai, and Hung-Lung Wang. On the Complexity of Finding 1-Center Spanning Trees. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 43:1-43:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lee_et_al:LIPIcs.WADS.2025.43,
  author =	{Lee, Pin-Hsian and Tsai, Meng-Tsung and Wang, Hung-Lung},
  title =	{{On the Complexity of Finding 1-Center Spanning Trees}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{43:1--43:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.43},
  URN =		{urn:nbn:de:0030-drops-242743},
  doi =		{10.4230/LIPIcs.WADS.2025.43},
  annote =	{Keywords: Treeradius, Spanning tree polytope, Shortest s, t-path polytope}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.65
Parameterized Spanning Tree Congestion

Authors: Michael Lampis, Valia Mitsou, Edouard Nemery, Yota Otachi, Manolis Vasilakis, and Daniel Vaz

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
In this paper we study the Spanning Tree Congestion problem, where we are given an undirected graph G = (V,E) and are asked to find a spanning tree T of minimum maximum congestion. Here, the congestion of an edge e ∈ T is the number of edges uv ∈ E such that the (unique) path from u to v in T traverses e. We consider this well-studied NP-hard problem from the point of view of (structural) parameterized complexity and obtain the following results: - We resolve a natural open problem by showing that Spanning Tree Congestion is not FPT parameterized by treewidth (under standard assumptions). More strongly, we present a generic reduction which applies to (almost) any parameter of the form "vertex-deletion distance to class 𝒞", thus obtaining W[1]-hardness for more restricted parameters, including tree-depth plus feedback vertex set, or incomparable to treewidth, such as twin cover. Via a slight tweak of the same reduction we also show that the problem is NP-complete on graphs of modular-width 4. - Even though it is known that Spanning Tree Congestion remains NP-hard on instances with only one vertex of unbounded degree, it is currently open whether the problem remains hard on bounded-degree graphs. We resolve this question by showing NP-hardness on graphs of maximum degree 8. - Complementing the problem’s W[1]-hardness for treewidth, we formulate an algorithm that runs in time roughly {(k+w)}^{𝒪(w)}, where k is the desired congestion and w the treewidth, improving a previous argument for parameter k+w that was based on Courcelle’s theorem. This explicit algorithm pays off in two ways: it allows us to obtain an FPT approximation scheme for parameter treewidth, that is, a (1+ε)-approximation running in time roughly {(w/ε)}^{𝒪(w)}; and it leads to an exact FPT algorithm for parameter clique-width+k via a Win/Win argument. - Finally, motivated by the problem’s hardness for most standard structural parameters, we present FPT algorithms for several more restricted cases, namely, for the parameters vertex-deletion distance to clique; vertex integrity; and feedback edge set, in the latter case also achieving a single-exponential running time dependence on the parameter.
Cite as

Michael Lampis, Valia Mitsou, Edouard Nemery, Yota Otachi, Manolis Vasilakis, and Daniel Vaz. Parameterized Spanning Tree Congestion. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 65:1-65:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lampis_et_al:LIPIcs.MFCS.2025.65,
  author =	{Lampis, Michael and Mitsou, Valia and Nemery, Edouard and Otachi, Yota and Vasilakis, Manolis and Vaz, Daniel},
  title =	{{Parameterized Spanning Tree Congestion}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{65:1--65:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.65},
  URN =		{urn:nbn:de:0030-drops-241724},
  doi =		{10.4230/LIPIcs.MFCS.2025.65},
  annote =	{Keywords: Parameterized Complexity, Treewidth, Graph Width Parameters}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.88
Color Refinement for Relational Structures

Authors: Benjamin Scheidt and Nicole Schweikardt

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Color Refinement, also known as Naive Vertex Classification, is a classical method to distinguish graphs by iteratively computing a coloring of their vertices. While it is traditionally used as an imperfect way to test for isomorphism, the algorithm has permeated many other, seemingly unrelated, areas of computer science. The method is algorithmically simple, and it has a well-understood distinguishing power: it has been logically characterized by Immerman and Lander (1990) and Cai, Fürer, Immerman (1992), who showed that it distinguishes precisely those graphs that can be distinguished by a sentence of first-order logic with counting quantifiers and only two variables. A combinatorial characterization was given by Dvořák (2010), who showed that it distinguishes precisely those graphs that differ in the number of homomorphisms from some tree. In this paper, we introduce Relational Color Refinement (RCR, for short), a generalization of the Color Refinement method from graphs to arbitrary relational structures, whose distinguishing power admits the equivalent combinatorial and logical characterizations as Color Refinement has on graphs: we show that RCR distinguishes precisely those structures that differ in the number of homomorphisms from an acyclic connected relational structure. Further, we show that RCR distinguishes precisely those structures that are distinguished by a sentence of the guarded fragment of first-order logic with counting quantifiers. Additionally, we show that for every fixed finite relational signature, RCR can be implemented to run on structures of that signature in time O(N⋅log N), where N denotes the number of tuples present in the structure.
Cite as

Benjamin Scheidt and Nicole Schweikardt. Color Refinement for Relational Structures. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 88:1-88:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{scheidt_et_al:LIPIcs.MFCS.2025.88,
  author =	{Scheidt, Benjamin and Schweikardt, Nicole},
  title =	{{Color Refinement for Relational Structures}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{88:1--88:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.88},
  URN =		{urn:nbn:de:0030-drops-241958},
  doi =		{10.4230/LIPIcs.MFCS.2025.88},
  annote =	{Keywords: color refinement, counting logics, homomorphism counts, homomorphism indistinguishability, guarded logics, pebble games, relational structures, alpha-acyclicity, join-trees}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.96
Asymptotically Optimal Inapproximability of Maxmin k-Cut Reconfiguration

Authors: Shuichi Hirahara and Naoto Ohsaka

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
k-Coloring Reconfiguration is one of the most well-studied reconfiguration problems, which asks to transform a given proper k-coloring of a graph to another by repeatedly recoloring a single vertex. Its approximate version, Maxmin k-Cut Reconfiguration, is defined as an optimization problem of maximizing the minimum fraction of bichromatic edges during the transformation between (not necessarily proper) k-colorings. In this paper, we demonstrate that the optimal approximation factor of this problem is 1 - Θ(1/k) for every k ≥ 2. Specifically, we prove the PSPACE-hardness of approximating the objective value within a factor of 1 - ε/k for some universal constant ε > 0, whereas we develop a deterministic polynomial-time algorithm that achieves the approximation factor of 1 - 2/k. To prove the hardness result, we propose a new probabilistic verifier that tests a "striped" pattern. Our approximation algorithm is based on a random transformation that passes through a random k-coloring.
Cite as

Shuichi Hirahara and Naoto Ohsaka. Asymptotically Optimal Inapproximability of Maxmin k-Cut Reconfiguration. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 96:1-96:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hirahara_et_al:LIPIcs.ICALP.2025.96,
  author =	{Hirahara, Shuichi and Ohsaka, Naoto},
  title =	{{Asymptotically Optimal Inapproximability of Maxmin k-Cut Reconfiguration}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{96:1--96:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.96},
  URN =		{urn:nbn:de:0030-drops-234733},
  doi =		{10.4230/LIPIcs.ICALP.2025.96},
  annote =	{Keywords: reconfiguration problems, graph coloring, hardness of approximation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.122
Yet Another Simple Proof of the PCRP Theorem

Authors: Naoto Ohsaka

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
The Probabilistically Checkable Reconfiguration Proof (PCRP) theorem, proven by Hirahara and Ohsaka (STOC 2024) [Hirahara and Ohsaka, 2024] and Karthik C. S. and Manurangsi [{Karthik {C. S.}} and Manurangsi, 2023], provides a new PCP-type characterization of PSPACE: A language L is in PSPACE if and only if there exists a probabilistic verifier 𝒱 and a pair of polynomial-time computable proofs π^ini, π^end such that the following hold for every input x: - If x ∈ L, then π^ini(x) can be transformed into π^end(x) by repeatedly flipping a single bit of the proof at a time, while making 𝒱(x) to accept every intermediate proof with probability 1. - If x ∉ L, then any such transformation induces a proof that is rejected by 𝒱(x) with probability more than 1/2. The PCRP theorem finds many applications in PSPACE-hardness of approximation for reconfiguration problems. In this paper, we present an alternative proof of the PCRP theorem that is "simpler" than those of Hirahara and Ohsaka [Hirahara and Ohsaka, 2024] and Karthik C. S. and Manurangsi [Karthik C. S. and Manurangsi, 2023]. Our PCRP system is obtained by combining simple robustization and composition steps in a modular fashion, which renders its analysis more intuitive. The crux of implementing the robustization step is an error-correcting code that enjoys both list decodability and reconfigurability, the latter of which enables to reconfigure between a pair of codewords, while avoiding getting too close to any other codewords.
Cite as

Naoto Ohsaka. Yet Another Simple Proof of the PCRP Theorem. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 122:1-122:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ohsaka:LIPIcs.ICALP.2025.122,
  author =	{Ohsaka, Naoto},
  title =	{{Yet Another Simple Proof of the PCRP Theorem}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{122:1--122:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.122},
  URN =		{urn:nbn:de:0030-drops-234995},
  doi =		{10.4230/LIPIcs.ICALP.2025.122},
  annote =	{Keywords: reconfiguration problems, hardness of approximation, probabilistic proof systems}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.71
Unfairly Splitting Separable Necklaces

Authors: Patrick Schnider, Linus Stalder, and Simon Weber

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
The Necklace Splitting problem is a classical problem in combinatorics that has been intensively studied both from a combinatorial and a computational point of view. It is well-known that the Necklace Splitting problem reduces to the discrete Ham Sandwich problem. This reduction was crucial in the proof of PPA-completeness of the Ham Sandwich problem. Recently, Borzechowski, Schnider and Weber [ISAAC'23] introduced a variant of Necklace Splitting that similarly reduces to the α-Ham Sandwich problem, which lies in the complexity class UEOPL but is not known to be complete. To make this reduction work, the input necklace is guaranteed to be n-separable. They showed that these necklaces can be fairly split in polynomial time and thus this subproblem cannot be used to prove UEOPL-hardness for α-Ham Sandwich. We consider the more general unfair necklace splitting problem on n-separable necklaces, i.e., the problem of splitting these necklaces such that each thief gets a desired fraction of each type of jewels. This more general problem is the natural necklace-splitting-type version of α-Ham Sandwich, and its complexity status is one of the main open questions posed by Borzechowski, Schnider and Weber. We show that the unfair splitting problem is also polynomial-time solvable, and can thus also not be used to show UEOPL-hardness for α-Ham Sandwich.
Cite as

Patrick Schnider, Linus Stalder, and Simon Weber. Unfairly Splitting Separable Necklaces. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 71:1-71:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{schnider_et_al:LIPIcs.STACS.2025.71,
  author =	{Schnider, Patrick and Stalder, Linus and Weber, Simon},
  title =	{{Unfairly Splitting Separable Necklaces}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{71:1--71:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.71},
  URN =		{urn:nbn:de:0030-drops-228963},
  doi =		{10.4230/LIPIcs.STACS.2025.71},
  annote =	{Keywords: Necklace splitting, n-separability, well-separation, Ham Sandwich, alpha-Ham Sandwich, unfair splitting, fair division}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.75
Canonical Labeling of Sparse Random Graphs

Authors: Oleg Verbitsky and Maksim Zhukovskii

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We show that if p = O(1/n), then the Erdős-Rényi random graph G(n,p) with high probability admits a canonical labeling computable in time O(nlog n). Combined with the previous results on the canonization of random graphs, this implies that G(n,p) with high probability admits a polynomial-time canonical labeling whatever the edge probability function p. Our algorithm combines the standard color refinement routine with simple post-processing based on the classical linear-time tree canonization. Noteworthy, our analysis of how well color refinement performs in this setting allows us to complete the description of the automorphism group of the 2-core of G(n,p).
Cite as

Oleg Verbitsky and Maksim Zhukovskii. Canonical Labeling of Sparse Random Graphs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 75:1-75:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{verbitsky_et_al:LIPIcs.STACS.2025.75,
  author =	{Verbitsky, Oleg and Zhukovskii, Maksim},
  title =	{{Canonical Labeling of Sparse Random Graphs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{75:1--75:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.75},
  URN =		{urn:nbn:de:0030-drops-229003},
  doi =		{10.4230/LIPIcs.STACS.2025.75},
  annote =	{Keywords: Graph isomorphism, random graphs, canonical labeling, color refinement}
}
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