17 Search Results for "Razgon, Igor"

Document
DOI: 10.4230/LIPIcs.IPEC.2025.29
Hitting Geodesic Intervals in Structurally Restricted Graphs

Authors: Tatsuya Gima, Yasuaki Kobayashi, Yuto Okada, Yota Otachi, and Hayato Takaike

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

Abstract
Given a graph G = (V,E), a set T of vertex pairs, and an integer k, Hitting Geodesic Intervals asks whether there is a set S ⊆ V of size at most k such that for each terminal pair {u,v} ∈ T, the set S intersects at least one shortest u-v path. Aravind and Saxena [WALCOM 2024] introduced this problem and showed several parameterized complexity results. In this paper, we extend the known results in both negative and positive directions and present sharp complexity contrasts with respect to structural graph parameters. We first show that the problem is NP-complete even on graphs with highly restricted shortest-path structures. More precisely, we show the NP-completeness on graphs obtained by adding a single vertex to a disjoint union of 5-vertex paths. By modifying the proof of this result, we also show the NP-completeness on graphs obtained from a path by adding one vertex and on graphs obtained from a disjoint union of triangles by adding one universal vertex. Furthermore, we show the NP-completeness on graphs of bandwidth 4 and maximum degree 5 by replacing the universal vertex in the last case with a long path. Under standard complexity assumptions, these negative results rule out fixed-parameter algorithms for most of the structural parameters studied in the literature (if the solution size k is not part of the parameter). We next present fixed-parameter algorithms parameterized by k plus modular-width and by k plus vertex integrity. The algorithm for the latter case does indeed solve a more general setting that includes the parameterization by the minimum vertex multiway-cut size of the terminal vertices. We show that this is tight in the sense that the problem parameterized by the minimum vertex multicut size of the terminal pairs is W[2]-complete. We then modify the proof of this intractability result and show that the problem is W[2]-complete parameterized by k even in the setting where T = binom(Q,2) for some Q ⊆ V.
Cite as

Tatsuya Gima, Yasuaki Kobayashi, Yuto Okada, Yota Otachi, and Hayato Takaike. Hitting Geodesic Intervals in Structurally Restricted Graphs. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gima_et_al:LIPIcs.IPEC.2025.29,
  author =	{Gima, Tatsuya and Kobayashi, Yasuaki and Okada, Yuto and Otachi, Yota and Takaike, Hayato},
  title =	{{Hitting Geodesic Intervals in Structurally Restricted Graphs}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{29:1--29:16},
  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.2025.29},
  URN =		{urn:nbn:de:0030-drops-251618},
  doi =		{10.4230/LIPIcs.IPEC.2025.29},
  annote =	{Keywords: Terminal monitoring set, Structural graph parameter, Geodesic interval}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.26
Complexity of Local Search for CSPs Parameterized by Constraint Difference

Authors: Aditya Anand, Vincent Cohen-Addad, Tommaso D'Orsi, Anupam Gupta, Euiwoong Lee, Debmalya Panigrahi, and Sijin Peng

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

Abstract
In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible subset S of a universe U, the new input consists of a current solution P (not necessarily feasible) as well as an ordinary input for the problem. Given the existence of a feasible solution S^*, the goal is to find a feasible solution as good as S^* in parameterized time f(k)⋅n^O(1), where k denotes the distance |PΔ S^*|. This model generalizes numerous classical parameterized optimization problems whose parameter k is the minimum number of elements removed from U to make it feasible, which corresponds to the case P = U. We apply this model to widely studied Constraint Satisfaction Problems (CSPs), where U is the set of constraints, and a subset U' of constraints is feasible if there is an assignment to the variables satisfying all constraints in U'. We give a complete characterization of the parameterized complexity of all boolean-alphabet symmetric CSPs, where the predicate’s acceptance depends on the number of true literals.
Cite as

Aditya Anand, Vincent Cohen-Addad, Tommaso D'Orsi, Anupam Gupta, Euiwoong Lee, Debmalya Panigrahi, and Sijin Peng. Complexity of Local Search for CSPs Parameterized by Constraint Difference. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{anand_et_al:LIPIcs.IPEC.2025.26,
  author =	{Anand, Aditya and Cohen-Addad, Vincent and D'Orsi, Tommaso and Gupta, Anupam and Lee, Euiwoong and Panigrahi, Debmalya and Peng, Sijin},
  title =	{{Complexity of Local Search for CSPs Parameterized by Constraint Difference}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{26:1--26:17},
  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.2025.26},
  URN =		{urn:nbn:de:0030-drops-251586},
  doi =		{10.4230/LIPIcs.IPEC.2025.26},
  annote =	{Keywords: Constraint Satisfaction Problems, Parameterized Local Search, Optimization}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.6
Boundaried Kernelization via Representative Sets

Authors: Leonid Antipov and Stefan Kratsch

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

Abstract
A kernelization is an efficient algorithm that given an instance of a parameterized problem returns an equivalent instance of size bounded by some function of the input parameter value. It is quite well understood which problems do or (conditionally) do not admit a kernelization where this size bound is polynomial, a so-called polynomial kernelization. Unfortunately, such polynomial kernelizations are known only in fairly restrictive settings where a small parameter value corresponds to a strong restriction on the global structure on the instance. Motivated by this, Antipov and Kratsch [WG 2025] proposed a local variant of kernelization, called boundaried kernelization, that requires only local structure to achieve a local improvement of the instance, which is in the spirit of protrusion replacement used in meta-kernelization [Bodlaender et al. JACM 2016]. They obtain polynomial boundaried kernelizations as well as (unconditional) lower bounds for several well-studied problems in kernelization. In this work, we leverage the matroid-based techniques of Kratsch and Wahlström [JACM 2020] to obtain randomized polynomial boundaried kernelizations for s-Multiway Cut, Deletable Terminal Multiway Cut, Odd Cycle Transversal, and Vertex Cover[oct], for which randomized polynomial kernelizations in the usual sense were known before. A priori, these techniques rely on the global connectivity of the graph to identify reducible (irrelevant) vertices. Nevertheless, the separation of the local part by its boundary turns out to be sufficient for a local application of these methods.
Cite as

Leonid Antipov and Stefan Kratsch. Boundaried Kernelization via Representative Sets. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{antipov_et_al:LIPIcs.IPEC.2025.6,
  author =	{Antipov, Leonid and Kratsch, Stefan},
  title =	{{Boundaried Kernelization via Representative Sets}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{6:1--6:13},
  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.2025.6},
  URN =		{urn:nbn:de:0030-drops-251386},
  doi =		{10.4230/LIPIcs.IPEC.2025.6},
  annote =	{Keywords: Parameterized complexity, boundaried kernelization, local preprocessing, representative sets method}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.39
Improved Approximation for Pathwidth One Vertex Deletion and Parameterized Complexity of Its Variants

Authors: Satyabrata Jana, Soumen Mandal, Ashutosh Rai, and Saket Saurabh

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

Abstract
The pathwidth of a graph is a measure of how path-like the graph is. The Pathwidth One Vertex Deletion (POVD) problem asks whether, given an undirected graph G and an integer k, one can delete at most k vertices from G so that the remaining graph has pathwidth at most one. This is a natural variation of the classical Feedback vertex Set (FVS) problem, where the deletion of at most k vertices results in a graph of treewidth at most one. In this work, we investigate POVD in the realm of approximation algorithms. We first design a 3-approximation algorithm for POVD running in polynomial time. Then, using this constant factor approximation algorithm, we obtain a randomized parameterized approximation algorithm for POVD running in time 𝒪^*((h_β)^k), that improves the fastest existing running times for approximation ratios in the range (1.76147,3). Here the constant h_β depends on the approximation factor β alone and has value 2^{(3-β)}, which lies in the range (1,2.3596), when β ∈ (1.76147,3). Taking inspiration from two extensively studied problems, namely Connected FVS and Independent FVS, we investigate two variations of the POVD problem from the perspective of parameterized algorithms. These variations are the connected variant, called Connected pathwidth One Vertex Deletion (CPOVD) and the independent variant, called Independent Pathwidth One Vertex Deletion (IPOVD). While in CPOVD the subgraph G[S] induced by the vertices to be deleted needs to be connected, in IPOVD it needs to be independent. Specifically, we show the following results. - CPOVD can be solved in {𝒪}^*(14^k) time and admits no polynomial kernel unless NP ⊆ {co-NP/poly}. - IPOVD can be solved in {𝒪}^*(7^k) time, and admits a kernel of size 𝒪(k³).
Cite as

Satyabrata Jana, Soumen Mandal, Ashutosh Rai, and Saket Saurabh. Improved Approximation for Pathwidth One Vertex Deletion and Parameterized Complexity of Its Variants. 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. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jana_et_al:LIPIcs.FSTTCS.2025.39,
  author =	{Jana, Satyabrata and Mandal, Soumen and Rai, Ashutosh and Saurabh, Saket},
  title =	{{Improved Approximation for Pathwidth One Vertex Deletion and Parameterized Complexity of Its Variants}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{39:1--39:20},
  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.2025.39},
  URN =		{urn:nbn:de:0030-drops-251192},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.39},
  annote =	{Keywords: Pathwidth, Parameterized complexity, Approximation, Kernelization}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.53
A Parameterized Study of Secluded Structures in Directed Graphs

Authors: Jonas Schmidt, Shaily Verma, and Nadym Mallek

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

Abstract
Given an undirected graph G and an integer k, the Secluded Π-Subgraph problem asks you to find a maximum size induced subgraph that satisfies a property Π and has at most k neighbors in the rest of the graph. This problem has been extensively studied; however, there is no prior study of the problem in directed graphs. This question has been mentioned by Jansen et al. [ISAAC'23]. In this paper, we initiate the study of Secluded Subgraph problems in directed graphs by incorporating different notions of neighborhoods: in-neighborhood, out-neighborhood, and their union. Formally, we call these problems {In, Out, Total}-Secluded Π-Subgraph, where given a directed graph G and an integer k, we want to find an induced subgraph satisfying Π of maximum size that has at most k in/out/total-neighbors in the rest of the graph, respectively. We investigate the parameterized complexity of these problems for different properties Π. In particular, we prove the following parameterized results: - We design an FPT algorithm for the Total-Secluded Strongly Connected Subgraph problem when parameterized by k. - We show that the Out-Secluded ℱ-Free Subgraph problem with parameter k is W[1]-hard, where ℱ is a family of directed graphs except any subgraph of a star graph whose edges are directed towards the center. This result also implies that In/Out-Secluded DAG is W[1]-hard, unlike the undirected variants of the two problems, which are FPT. - We design an FPT-algorithm for In/Out/Total-Secluded α-Bounded Subgraph when parameterized by k, where α-bounded graphs are a superclass of tournaments. - For undirected graphs, we improve the best-known FPT algorithm for Secluded Clique by providing a faster FPT algorithm that runs in time 1.6181^k n^𝒪(1).
Cite as

Jonas Schmidt, Shaily Verma, and Nadym Mallek. A Parameterized Study of Secluded Structures in Directed Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 53:1-53:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{schmidt_et_al:LIPIcs.ISAAC.2025.53,
  author =	{Schmidt, Jonas and Verma, Shaily and Mallek, Nadym},
  title =	{{A Parameterized Study of Secluded Structures in Directed Graphs}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{53:1--53:21},
  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.2025.53},
  URN =		{urn:nbn:de:0030-drops-249616},
  doi =		{10.4230/LIPIcs.ISAAC.2025.53},
  annote =	{Keywords: Secluded Subgraph, Parametrized Complexity, Directed Graphs, Strong Connectivity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.88
Parameterized Approximability for Modular Linear Equations

Authors: Konrad K. Dabrowski, Peter Jonsson, Sebastian Ordyniak, George Osipov, and Magnus Wahlström

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

Abstract
We consider the Min-r-Lin(ℤ_m) problem: given a system S of length-r linear equations modulo m, find Z ⊆ S of minimum cardinality such that S-Z is satisfiable. The problem is NP-hard and UGC-hard to approximate in polynomial time within any constant factor even when r = m = 2. We focus on parameterized approximation with solution size as the parameter. Dabrowski, Jonsson, Ordyniak, Osipov and Wahlström [SODA-2023] showed that Min-r-Lin(ℤ_m) is in FPT if m is prime (i.e. ℤ_m is a field), and it is W[1]-hard if m is not a prime power. We show that Min-r-Lin(ℤ_{pⁿ}) is FPT-approximable within a factor of 2 for every prime p and integer n ≥ 2. This implies that Min-2-Lin(ℤ_m), m ∈ ℤ^+, is FPT-approximable within a factor of 2ω(m) where ω(m) counts the number of distinct prime divisors of m. The high-level idea behind the algorithm is to solve tighter and tighter relaxations of the problem, decreasing the set of possible values for the variables at each step. When working over ℤ_{pⁿ} and viewing the values in base-p, one can roughly think of a relaxation as fixing the number of trailing zeros and the least significant nonzero digits of the values assigned to the variables. To solve the relaxed problem, we construct a certain graph where solutions can be identified with a particular collection of cuts. The relaxation may hide obstructions that will only become visible in the next iteration of the algorithm, which makes it difficult to find optimal solutions. To deal with this, we use a strategy based on shadow removal [Marx & Razgon, STOC-2011] to compute solutions that (1) cost at most twice as much as the optimum and (2) allow us to reduce the set of values for all variables simultaneously. We complement the algorithmic result with two lower bounds, ruling out constant-factor FPT-approximation for Min-3-Lin(R) over any nontrivial ring R and for Min-2-Lin(R) over some finite commutative rings R.
Cite as

Konrad K. Dabrowski, Peter Jonsson, Sebastian Ordyniak, George Osipov, and Magnus Wahlström. Parameterized Approximability for Modular Linear Equations. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 88:1-88:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dabrowski_et_al:LIPIcs.ESA.2025.88,
  author =	{Dabrowski, Konrad K. and Jonsson, Peter and Ordyniak, Sebastian and Osipov, George and Wahlstr\"{o}m, Magnus},
  title =	{{Parameterized Approximability for Modular Linear Equations}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{88:1--88:15},
  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.2025.88},
  URN =		{urn:nbn:de:0030-drops-245562},
  doi =		{10.4230/LIPIcs.ESA.2025.88},
  annote =	{Keywords: parameterized complexity, approximation algorithms, linear equations}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.70
Labelled Well Quasi Ordered Classes of Bounded Linear Clique-Width

Authors: Aliaume Lopez

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

Abstract
We construct an algorithm that inputs an MSO-interpretation from finite words to graphs, and decides if there exists a k ∈ ℕ such that the class of graphs induced by the interpretation is not well-quasi-ordered by the induced subgraph relation when vertices are freely labelled using {1, …, k}. In case no such k exists, we also prove that the class of graphs is not well-quasi-ordered by the induced subgraph relation when vertices are freely labelled using any well-quasi-ordered set of labels. As a byproduct of our analysis, we prove that for classes of bounded linear clique-width, a weak version of a conjecture by Pouzet holds.
Cite as

Aliaume Lopez. Labelled Well Quasi Ordered Classes of Bounded Linear Clique-Width. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 70:1-70:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lopez:LIPIcs.MFCS.2025.70,
  author =	{Lopez, Aliaume},
  title =	{{Labelled Well Quasi Ordered Classes of Bounded Linear Clique-Width}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{70:1--70:17},
  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.2025.70},
  URN =		{urn:nbn:de:0030-drops-241773},
  doi =		{10.4230/LIPIcs.MFCS.2025.70},
  annote =	{Keywords: well-quasi-ordering, linear clique-width, MSO transduction, automata theory}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.25
Mim-Width Is paraNP-Complete

Authors: Benjamin Bergougnoux, Édouard Bonnet, and Julien Duron

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

Abstract
We show that it is NP-hard to distinguish graphs of linear mim-width at most 1211 from graphs of sim-width at least 1216. This implies that Mim-Width, Sim-Width, One-Sided Mim-Width, and their linear counterparts are all paraNP-complete, i.e., NP-complete to compute even when upper bounded by a constant. A key intermediate problem that we introduce and show NP-complete, Linear Degree Balancing, inputs an edge-weighted graph G and an integer τ, and asks whether V(G) can be linearly ordered such that every vertex of G has weighted backward and forward degrees at most τ.
Cite as

Benjamin Bergougnoux, Édouard Bonnet, and Julien Duron. Mim-Width Is paraNP-Complete. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bergougnoux_et_al:LIPIcs.ICALP.2025.25,
  author =	{Bergougnoux, Benjamin and Bonnet, \'{E}douard and Duron, Julien},
  title =	{{Mim-Width Is paraNP-Complete}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{25:1--25:17},
  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.2025.25},
  URN =		{urn:nbn:de:0030-drops-234020},
  doi =		{10.4230/LIPIcs.ICALP.2025.25},
  annote =	{Keywords: Mim-width, lower bounds, parameterized complexity, ordered graphs}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.12
All-Subsets Important Separators with Applications to Sample Sets, Balanced Separators and Vertex Sparsifiers in Directed Graphs

Authors: Aditya Anand, Euiwoong Lee, Jason Li, and Thatchaphol Saranurak

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

Abstract
Given a directed graph G with n vertices and m edges, a parameter k and two disjoint subsets S,T ⊆ V(G), we show that the number of all-subsets important separators, which is the number of A-B important vertex separators of size at most k over all A ⊆ S and B ⊆ T, is at most β(|S|, |T|, k) = 4^k binom(|S|, ≤ k) binom(|T|, ≤ 2k), where binom(x, ≤ c) = ∑_{i = 1}^c binom(x,i), and that they can be enumerated in time 𝒪(β(|S|,|T|,k)k²(m+n)). This is a generalization of the folklore result stating that the number of A-B important separators for two fixed sets A and B is at most 4^k (first implicitly shown by Chen, Liu and Lu Algorithmica '09). From this result, we obtain the following applications: 1) We give a construction for detection sets and sample sets in directed graphs, generalizing the results of Kleinberg (Internet Mathematics' 03) and Feige and Mahdian (STOC' 06) to directed graphs. 2) Via our new sample sets, we give the first FPT algorithm for finding balanced separators in directed graphs parameterized by k, the size of the separator. Our algorithm runs in time 2^{𝒪(k)} ⋅ (m + n). 3) Additionally, we show a 𝒪(√{log k}) approximation algorithm for finding balanced separators in directed graphs in polynomial time. This improves the best known approximation guarantee of 𝒪(√{log n}) and matches the known guarantee in undirected graphs by Feige, Hajiaghayi and Lee (SICOMP' 08). 4) Finally, using our algorithm for listing all-subsets important separators, we give a deterministic construction of vertex cut sparsifiers in directed graphs when we are interested in preserving min-cuts of size upto c between bipartitions of the terminal set. Our algorithm constructs a sparsifier of size 𝒪(binom(t, ≤ 3c)2^{𝒪(c)}) and runs in time 𝒪(binom(t, ≤ 3c) 2^{𝒪(c)}(m + n)), where t is the number of terminals, and the sparsifier additionally preserves the set of important separators of size at most c between bipartitions of the terminals.
Cite as

Aditya Anand, Euiwoong Lee, Jason Li, and Thatchaphol Saranurak. All-Subsets Important Separators with Applications to Sample Sets, Balanced Separators and Vertex Sparsifiers in Directed Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{anand_et_al:LIPIcs.ICALP.2025.12,
  author =	{Anand, Aditya and Lee, Euiwoong and Li, Jason and Saranurak, Thatchaphol},
  title =	{{All-Subsets Important Separators with Applications to Sample Sets, Balanced Separators and Vertex Sparsifiers in Directed Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{12:1--12:20},
  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.2025.12},
  URN =		{urn:nbn:de:0030-drops-233892},
  doi =		{10.4230/LIPIcs.ICALP.2025.12},
  annote =	{Keywords: directed graphs, important separators, sample sets, balanced separators}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.16
Temporal Dominating Set and Temporal Vertex Cover Under the Lense of Degree Restrictions

Authors: Anton Herrmann, Christian Komusiewicz, Nils Morawietz, and Frank Sommer

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
We study the Temporal Dominating Set problem, in which one asks whether a temporal graph 𝒢 = (G₁,… , G_T) given as a sequence of snapshot graphs, over the same vertex set V, has a set S of temporal vertices of size at most k such that each vertex v of V is dominated by some w ∈ S in the snapshot that contains w. Additionally, we consider Temporal Partial Dominating Set, where one asks whether at least t (and not necessarily all) vertices of V can be dominated by S and a further generalization in which the solution may only contain a bounded number of temporal vertices from each snapshot. We analyze how the complexity of Temporal (Partial) Dominating Set is influenced by the maximum snapshot degree and the structure of the underlying graph, the graph with vertex set V and whose edge set is the union of all snapshot edge sets. For example, we obtain a complexity dichotomy for the maximum snapshot degree and we show that Temporal Partial Dominating Set is fixed-parameter tractable for tw+Δ, where tw and Δ denote the treewidth and the maximum degree of the underlying graph of 𝒢, respectively. We also show which of our results transfer to the well-studied Temporal Vertex Cover problem. For example, we show that Temporal Vertex Cover is also fixed-parameter tractable for tw+Δ which substantially extends the previously known polynomial-time algorithms for the case that the underlying graph is a path or cycle.
Cite as

Anton Herrmann, Christian Komusiewicz, Nils Morawietz, and Frank Sommer. Temporal Dominating Set and Temporal Vertex Cover Under the Lense of Degree Restrictions. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{herrmann_et_al:LIPIcs.SAND.2025.16,
  author =	{Herrmann, Anton and Komusiewicz, Christian and Morawietz, Nils and Sommer, Frank},
  title =	{{Temporal Dominating Set and Temporal Vertex Cover Under the Lense of Degree Restrictions}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.16},
  URN =		{urn:nbn:de:0030-drops-230695},
  doi =		{10.4230/LIPIcs.SAND.2025.16},
  annote =	{Keywords: NP-hard problem, FPT-algorithm, Treewidth, Color coding}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.36
MaxMin Separation Problems: FPT Algorithms for st-Separator and Odd Cycle Transversal

Authors: Ajinkya Gaikwad, Hitendra Kumar, Soumen Maity, Saket Saurabh, and Roohani Sharma

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

Abstract
In this paper, we study the parameterized complexity of the MaxMin versions of two fundamental separation problems: Maximum Minimal st-Separator and Maximum Minimal Odd Cycle Transversal (OCT), both parameterized by the solution size. In the Maximum Minimal st-Separator problem, given a graph G, two distinct vertices s and t and a positive integer k, the goal is to determine whether there exists a minimal st-separator in G of size at least k. Similarly, the Maximum Minimal OCT problem seeks to determine if there exists a minimal set of vertices whose deletion results in a bipartite graph, and whose size is at least k. We demonstrate that both problems are fixed-parameter tractable parameterized by k. Our FPT algorithm for Maximum Minimal st-Separator answers the open question by Hanaka, Bodlaender, van der Zanden & Ono [TCS 2019]. One unique insight from this work is the following. We use the meta-result of Lokshtanov, Ramanujan, Saurabh & Zehavi [ICALP 2018] that enables us to reduce our problems to highly unbreakable graphs. This is interesting, as an explicit use of the recursive understanding and randomized contractions framework of Chitnis, Cygan, Hajiaghayi, Pilipczuk & Pilipczuk [SICOMP 2016] to reduce to the highly unbreakable graphs setting (which is the result that Lokshtanov et al. tries to abstract out in their meta-theorem) does not seem obvious because certain "extension" variants of our problems are W[1]-hard.
Cite as

Ajinkya Gaikwad, Hitendra Kumar, Soumen Maity, Saket Saurabh, and Roohani Sharma. MaxMin Separation Problems: FPT Algorithms for st-Separator and Odd Cycle Transversal. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 36:1-36:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gaikwad_et_al:LIPIcs.STACS.2025.36,
  author =	{Gaikwad, Ajinkya and Kumar, Hitendra and Maity, Soumen and Saurabh, Saket and Sharma, Roohani},
  title =	{{MaxMin Separation Problems: FPT Algorithms for st-Separator and Odd Cycle Transversal}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{36:1--36:21},
  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.2025.36},
  URN =		{urn:nbn:de:0030-drops-228622},
  doi =		{10.4230/LIPIcs.STACS.2025.36},
  annote =	{Keywords: Parameterized Complexity, FPT, MaxMin problems, Maximum Minimal st-separator, Maximum Minimal Odd Cycle Transversal, Unbreakable Graphs, CMSO, Long Induced Odd Cycles, Sunflower Lemma}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.21
Adjacency Labeling Schemes for Small Classes

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

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
A graph class admits an implicit representation if, for every positive integer n, its n-vertex graphs have a O(log n)-bit (adjacency) labeling scheme, i.e., their vertices can be labeled by binary strings of length O(log n) such that the presence of an edge between any pair of vertices can be deduced solely from their labels. The famous Implicit Graph Conjecture posited that every hereditary (i.e., closed under taking induced subgraphs) factorial (i.e., containing 2^O(n log n) n-vertex graphs) class admits an implicit representation. The conjecture was recently refuted [Hatami and Hatami, FOCS '22], and does not even hold among monotone (i.e., closed under taking subgraphs) factorial classes [Bonnet et al., ICALP '24]. However, monotone small (i.e., containing at most n! cⁿ many n-vertex graphs for some constant c) classes do admit implicit representations. This motivates the Small Implicit Graph Conjecture: Every hereditary small class admits an O(log n)-bit labeling scheme. We provide evidence supporting the Small Implicit Graph Conjecture. First, we show that every small weakly sparse (i.e., excluding some fixed bipartite complete graph as a subgraph) class has an implicit representation. This is a consequence of the following fact of independent interest proved in the paper: Every weakly sparse small class has bounded expansion (hence, in particular, bounded degeneracy). Second, we show that every hereditary small class admits an O(log³ n)-bit labeling scheme, which provides a substantial improvement of the best-known polynomial upper bound of n^(1-ε) on the size of adjacency labeling schemes for such classes. This is a consequence of another fact of independent interest proved in the paper: Every small class has neighborhood complexity O(n log n).
Cite as

Édouard Bonnet, Julien Duron, John Sylvester, and Viktor Zamaraev. Adjacency Labeling Schemes for Small Classes. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonnet_et_al:LIPIcs.ITCS.2025.21,
  author =	{Bonnet, \'{E}douard and Duron, Julien and Sylvester, John and Zamaraev, Viktor},
  title =	{{Adjacency Labeling Schemes for Small Classes}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{21:1--21:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.21},
  URN =		{urn:nbn:de:0030-drops-226493},
  doi =		{10.4230/LIPIcs.ITCS.2025.21},
  annote =	{Keywords: Adjacency labeling, degeneracy, weakly sparse classes, small classes, implicit graph conjecture}
}
Document
DOI: 10.4230/LIPIcs.STACS.2024.48
FPT Approximation of Generalised Hypertree Width for Bounded Intersection Hypergraphs

Authors: Matthias Lanzinger and Igor Razgon

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
Generalised hypertree width (ghw) is a hypergraph parameter that is central to the tractability of many prominent problems with natural hypergraph structure. Computing ghw of a hypergraph is notoriously hard. The decision version of the problem, checking whether ghw(H) ≤ k, is paraNP-hard when parameterised by k. Furthermore, approximation of ghw is at least as hard as approximation of Set-Cover, which is known to not admit any FPT approximation algorithms. Research in the computation of ghw so far has focused on identifying structural restrictions to hypergraphs - such as bounds on the size of edge intersections - that permit XP algorithms for ghw. Yet, even under these restrictions that problem has so far evaded any kind of FPT algorithm. In this paper we make the first step towards FPT algorithms for ghw by showing that the parameter can be approximated in FPT time for graphs of bounded edge intersection size. In concrete terms we show that there exists an FPT algorithm, parameterised by k and d, that for input hypergraph H with maximal cardinality of edge intersections d and integer k either outputs a tree decomposition with ghw(H) ≤ 4k(k+d+1)(2k-1), or rejects, in which case it is guaranteed that ghw(H) > k. Thus, in the special case of hypergraphs of bounded edge intersection, we obtain an FPT O(k³)-approximation algorithm for ghw.
Cite as

Matthias Lanzinger and Igor Razgon. FPT Approximation of Generalised Hypertree Width for Bounded Intersection Hypergraphs. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 48:1-48:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{lanzinger_et_al:LIPIcs.STACS.2024.48,
  author =	{Lanzinger, Matthias and Razgon, Igor},
  title =	{{FPT Approximation of Generalised Hypertree Width for Bounded Intersection Hypergraphs}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{48:1--48:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.48},
  URN =		{urn:nbn:de:0030-drops-197588},
  doi =		{10.4230/LIPIcs.STACS.2024.48},
  annote =	{Keywords: generalized hypertree width, hypergraphs, parameterized algorithms, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2021.25
Classification of OBDD Size for Monotone 2-CNFs

Authors: Igor Razgon

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

Abstract
We introduce a new graph parameter called linear upper maximum induced matching width lu-mim width, denoted for a graph G by lu(G). We prove that the smallest size of the obdd for φ, the monotone 2-cnf corresponding to G, is sandwiched between 2^{lu(G)} and n^{O(lu(G))}. The upper bound is based on a combinatorial statement that might be of an independent interest. We show that the bounds in terms of this parameter are best possible. The new parameter is closely related to two existing parameters: linear maximum induced matching width (lmim width) and linear special induced matching width (lsim width). We prove that lu-mim width lies strictly in between these two parameters, being dominated by lsim width and dominating lmim width. We conclude that neither of the two existing parameters can be used instead of lu-mim width to characterize the size of obdds for monotone 2-cnfs and this justifies introduction of the new parameter.
Cite as

Igor Razgon. Classification of OBDD Size for Monotone 2-CNFs. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 25:1-25:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{razgon:LIPIcs.IPEC.2021.25,
  author =	{Razgon, Igor},
  title =	{{Classification of OBDD Size for Monotone 2-CNFs}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{25:1--25:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.25},
  URN =		{urn:nbn:de:0030-drops-154081},
  doi =		{10.4230/LIPIcs.IPEC.2021.25},
  annote =	{Keywords: Ordered Binary Decision Diagrams, Monotone 2-CNFs, Width parameters of graphs, upper and lower bounds}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.41
Fractional Covers of Hypergraphs with Bounded Multi-Intersection

Authors: Georg Gottlob, Matthias Lanzinger, Reinhard Pichler, and Igor Razgon

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
Fractional (hyper-)graph theory is concerned with the specific problems that arise when fractional analogues of otherwise integer-valued (hyper-)graph invariants are considered. The focus of this paper is on fractional edge covers of hypergraphs. Our main technical result generalizes and unifies previous conditions under which the size of the support of fractional edge covers is bounded independently of the size of the hypergraph itself. This allows us to extend previous tractability results for checking if the fractional hypertree width of a given hypergraph is ≤ k for some constant k. We also show how our results translate to fractional vertex covers.
Cite as

Georg Gottlob, Matthias Lanzinger, Reinhard Pichler, and Igor Razgon. Fractional Covers of Hypergraphs with Bounded Multi-Intersection. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 41:1-41:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gottlob_et_al:LIPIcs.MFCS.2020.41,
  author =	{Gottlob, Georg and Lanzinger, Matthias and Pichler, Reinhard and Razgon, Igor},
  title =	{{Fractional Covers of Hypergraphs with Bounded Multi-Intersection}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{41:1--41:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.41},
  URN =		{urn:nbn:de:0030-drops-127317},
  doi =		{10.4230/LIPIcs.MFCS.2020.41},
  annote =	{Keywords: Fractional graph theory, fractional edge cover, fractional hypertree width, bounded multi-intersection, fractional cover, fractional vertex cover}
}
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