15 Search Results for "van Rooij, Johan M. M."

Document
DOI: 10.4230/LIPIcs.STACS.2026.79
Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More

Authors: Mihail Stoian

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

Abstract
Despite much research, hard weighted problems still resist super-polynomial improvements over their textbook solution. On the other hand, the unweighted versions of these problems have recently witnessed the sought-after speedups. Currently, the only way to repurpose the algorithm of the unweighted version for the weighted version is to employ a polynomial embedding of the input weights. This, however, introduces a pseudo-polynomial factor into the running time, which becomes impractical for arbitrarily weighted instances. In this paper, we introduce a new way to repurpose the algorithm of the unweighted problem. Specifically, we show that the time complexity of several well-known NP-hard problems operating over the (min, +) and (max, +) semirings, such as TSP, Weighted Max-Cut, and Edge-Weighted k-Clique, is proportional to that of their unweighted versions when the set of input weights has small doubling. We achieve this by a meta-algorithm that converts the input weights into polynomially bounded integers using the recent constructive Freiman’s theorem by Randolph and Węgrzycki [ESA 2024] before applying the polynomial embedding.
Cite as

Mihail Stoian. Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 79:1-79:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{stoian:LIPIcs.STACS.2026.79,
  author =	{Stoian, Mihail},
  title =	{{Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{79:1--79:19},
  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.2026.79},
  URN =		{urn:nbn:de:0030-drops-255680},
  doi =		{10.4230/LIPIcs.STACS.2026.79},
  annote =	{Keywords: doubling constant parametrization, weighted problems, traveling salesman, weighted max-cut, edge-weighted k-clique}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.18
Bridging Treewidth and Clique-Width via Cograph-Modular-Treewidth

Authors: Václav Blažej, Satyabrata Jana, M. S. Ramanujan, and Peter Strulo

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

Abstract
Many classical graph problems - such as Max Cut, Chromatic Number, Edge Dominating Set, and Hamiltonian Cycle - are polynomial-time solvable on cographs, fixed-parameter tractable (FPT) when parameterized by treewidth, but W[1]-hard when parameterized by clique-width. In contrast, Graph Isomorphism is FPT parameterized by treewidth, but for clique-width it is known to be in XP; whether it is FPT or W[1]-hard is open. This reveals a sharp tractability gap between treewidth and clique-width. In this work, we propose a new structural graph parameter, 𝒞-modular-treewidth, which lies between treewidth and clique-width. The parameter leverages modular decomposition and restricts modules to induce graphs from a fixed class 𝒞 (e.g., cographs or edgeless graphs). By exploiting true and false twins - a hallmark of cograph-like structure - our parameter allows the design of efficient algorithms for several hard problems beyond the reach of treewidth-based methods. In this work, we show that 𝒞-modular-treewidth enables efficient solutions under suitable choices of 𝒞, opening a new pathway in the parameterized complexity landscape between treewidth and clique-width. In particular we show that - When parameterized by cograph-modular-treewidth, Isomorphism admits an FPT algorithm, whereas Chromatic Number remains W[1]-hard. - When parameterized by independent-modular-treewidth, Hamiltonian Cycle and Edge Dominating Set remain W[1]-hard.
Cite as

Václav Blažej, Satyabrata Jana, M. S. Ramanujan, and Peter Strulo. Bridging Treewidth and Clique-Width via Cograph-Modular-Treewidth. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{blazej_et_al:LIPIcs.IPEC.2025.18,
  author =	{Bla\v{z}ej, V\'{a}clav and Jana, Satyabrata and Ramanujan, M. S. and Strulo, Peter},
  title =	{{Bridging Treewidth and Clique-Width via Cograph-Modular-Treewidth}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{18:1--18:18},
  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.2025.18},
  URN =		{urn:nbn:de:0030-drops-251507},
  doi =		{10.4230/LIPIcs.IPEC.2025.18},
  annote =	{Keywords: Treewidth, Clique-width, Cograph, FPT, W\lbrack1\rbrack-hard}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.19
Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width

Authors: Narek Bojikian and Stefan Kratsch

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

Abstract
Recently, Bojikian and Kratsch [ICALP 2024] presented a novel approach to tackle connectivity problems parameterized by clique-width (cw), based on counting (modulo 2) the number of representations of partial solutions, while allowing for possibly multiple representations to exist for the same partial solution. Using this technique, they got a SETH-tight bound of 𝒪^*(3^{cw}) for the Steiner Tree problem, which was left open by Hegerfeld and Kratsch [ESA 2023]. We use the same technique to solve the Connected Odd Cycle Transversal problem in time 𝒪^*(12^{cw}). Moreover, we prove that our result is tight by providing a SETH-based lower bound excluding algorithms with running time 𝒪^*((12-ε)^{cw}). This answers another question of Hegerfeld and Kratsch [ESA 2023].
Cite as

Narek Bojikian and Stefan Kratsch. Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bojikian_et_al:LIPIcs.IPEC.2025.19,
  author =	{Bojikian, Narek and Kratsch, Stefan},
  title =	{{Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{19:1--19:15},
  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.2025.19},
  URN =		{urn:nbn:de:0030-drops-251516},
  doi =		{10.4230/LIPIcs.IPEC.2025.19},
  annote =	{Keywords: Parameterized complexity, connected odd cycle transversal, clique-width}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.30
A Graph Width Perspective on Partially Ordered Hamiltonian Paths and Cycles II: Vertex and Edge Deletion Numbers

Authors: Jesse Beisegel, Katharina Klost, Kristin Knorr, Fabienne Ratajczak, and Robert Scheffler

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

Abstract
We consider the problem of finding a Hamiltonian path or cycle with precedence constraints in the form of a partial order on the vertex set. We study the complexity for graph width parameters for which the ordinary problems Hamiltonian Path and Hamiltonian Cycle are in FPT. In particular, we focus on parameters that describe how many vertices and edges have to be deleted to become a member of a certain graph class. We show that the problems are W[1]-hard for such restricted cases as vertex distance to path and vertex distance to clique. We complement these results by showing that the problems can be solved in XP time for vertex distance to outerplanar and vertex distance to block. Furthermore, we present some FPT algorithms, e.g., for edge distance to block. Additionally, we prove para-NP-hardness when considered with the edge clique cover number.
Cite as

Jesse Beisegel, Katharina Klost, Kristin Knorr, Fabienne Ratajczak, and Robert Scheffler. A Graph Width Perspective on Partially Ordered Hamiltonian Paths and Cycles II: Vertex and Edge Deletion Numbers. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{beisegel_et_al:LIPIcs.IPEC.2025.30,
  author =	{Beisegel, Jesse and Klost, Katharina and Knorr, Kristin and Ratajczak, Fabienne and Scheffler, Robert},
  title =	{{A Graph Width Perspective on Partially Ordered Hamiltonian Paths and Cycles II: Vertex and Edge Deletion Numbers}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{30:1--30:19},
  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.2025.30},
  URN =		{urn:nbn:de:0030-drops-251623},
  doi =		{10.4230/LIPIcs.IPEC.2025.30},
  annote =	{Keywords: Hamiltonian path, Hamiltonian cycle, partial order, graph width parameter, parameterized complexity}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.32
The PACE 2025 Parameterized Algorithms and Computational Experiments Challenge: Dominating Set and Hitting Set

Authors: Mario Grobler and Sebastian Siebertz

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

Abstract
The 10th iteration of the of the Parameterized Algorithms and Computational Experiments challenge (PACE) 2025 was devoted to engineer algorithms solving the Dominating Set problem as well as the Hitting Set problem. In contrast to the last iterations, these problems are (under standard assumptions) not fixed-parameter tractable (fpt) in general. However, restricting the structure of the input (e.g. to planar graphs or degenerate graphs for Dominating Set, or to set systems with sets of bounded size for Hitting Set) renders these problems fpt. Following the spirit of the last iterations of the PACE challenge, there is an exact track and a heuristic track for each problem; each track coming with a benchmark set of 100 public instances and 100 private instances. Overall, the PACE 2025 had 71 participants from 25 teams, 13 countries, and 3 continents. In this report, we briefly describe the setup of the challenge, the selection of benchmark instances, as well as the ranking of the participating teams. We also briefly outline the approaches used in the submitted solvers.
Cite as

Mario Grobler and Sebastian Siebertz. The PACE 2025 Parameterized Algorithms and Computational Experiments Challenge: Dominating Set and Hitting Set. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 32:1-32:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{grobler_et_al:LIPIcs.IPEC.2025.32,
  author =	{Grobler, Mario and Siebertz, Sebastian},
  title =	{{The PACE 2025 Parameterized Algorithms and Computational Experiments Challenge: Dominating Set and Hitting Set}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{32:1--32:17},
  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.2025.32},
  URN =		{urn:nbn:de:0030-drops-251644},
  doi =		{10.4230/LIPIcs.IPEC.2025.32},
  annote =	{Keywords: PACE 2025 Report, Dominating Set, Hitting Set, Algorithm Engineering, FPT, Heuristics}
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2025.35
PACE Solver Description: Bad Dominating Set Maker

Authors: Alexander Dobler, Simon Dominik Fink, and Mathis Rocton

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

Abstract
Dominating Set and Hitting Set are two well-known NP-hard problems on graphs and hypergraphs, respectively. For Dominating Set, we seek a subset S of vertices of minimum size, such that every vertex has a neighbor in S. For Hitting Set, we require that this minimum size subset S intersects each hyperedge. We present Bad Dominating Set Maker, our solver for both problems posed in the exact tracks of the 2025 PACE Challenge. It uses reduction rules, dynamic programming on tree decompositions, and external Vertex Cover and SAT solvers.
Cite as

Alexander Dobler, Simon Dominik Fink, and Mathis Rocton. PACE Solver Description: Bad Dominating Set Maker. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 35:1-35:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dobler_et_al:LIPIcs.IPEC.2025.35,
  author =	{Dobler, Alexander and Fink, Simon Dominik and Rocton, Mathis},
  title =	{{PACE Solver Description: Bad Dominating Set Maker}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{35:1--35:5},
  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.2025.35},
  URN =		{urn:nbn:de:0030-drops-251673},
  doi =		{10.4230/LIPIcs.IPEC.2025.35},
  annote =	{Keywords: Dominating Set, Hitting Set, Pace Challenge}
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2025.36
PACE Solver Description: Reductions and Heuristic Search for the Dominating Set Problem and the Hitting Set Problem

Authors: Florian Fontan and Guillaume Verger

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

Abstract
In this paper, we describe the solver we submitted for both heuristic tracks of the PACE challenge 2025 on the dominating set problem and the hitting set problem. We solve both problems as unicost set covering problems. Our solver first performs reductions on the instance. Then greedy algorithms generate an initial solution that serves as starting point of the large neighborhood search and the local search which are executed afterwards. The solver ranked first in the dominating set heuristic track, and second in the hitting set heuristic track.
Cite as

Florian Fontan and Guillaume Verger. PACE Solver Description: Reductions and Heuristic Search for the Dominating Set Problem and the Hitting Set Problem. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 36:1-36:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fontan_et_al:LIPIcs.IPEC.2025.36,
  author =	{Fontan, Florian and Verger, Guillaume},
  title =	{{PACE Solver Description: Reductions and Heuristic Search for the Dominating Set Problem and the Hitting Set Problem}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{36:1--36:3},
  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.2025.36},
  URN =		{urn:nbn:de:0030-drops-251681},
  doi =		{10.4230/LIPIcs.IPEC.2025.36},
  annote =	{Keywords: dominating set, hitting set, unicost set covering, reductions, large neighborhood search, local search}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.43
A Finer View of the Parameterized Landscape of Labeled Graph Contractions

Authors: Yashaswini Mathur and Prafullkumar Tale

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

Abstract
We study the Labeled Contractibility problem, where the input consists of two vertex-labeled graphs G and H, and the goal is to determine whether H can be obtained from G via a sequence of edge contractions. Lafond and Marchand [WADS 2025] initiated the parameterized complexity study of this problem, showing it to be W[1]-hard when parameterized by the number k of allowed contractions. They also proved that the problem is fixed-parameter tractable when parameterized by the tree-width tw of G, via an application of Courcelle’s theorem resulting in a non-constructive algorithm. In this work, we present a constructive fixed-parameter algorithm for Labeled Contractibility with running time 2^{𝒪(tw²)} ⋅ |V(G)|^{𝒪(1)}. We also prove that unless the Exponential Time Hypothesis ({ETH}) fails, it does not admit an algorithm running in time 2^{o(tw²)} ⋅ |V(G)|^{𝒪(1)}. This result adds Labeled Contractibility to a small list of problems that admit such a lower bound and matching algorithm. We further strengthen existing hardness results by showing that the problem remains NP-complete even when both input graphs have bounded maximum degree. We also investigate parameterizations by (k + δ(G)) where δ(G) denotes the degeneracy of G, and rule out the existence of subexponential-time algorithms. This answers question raised in Lafond and Marchand [WADS 2025]. We additionally provide an improved FPT algorithm with better dependence on (k + δ(G)) than previously known. Finally, we analyze a brute-force algorithm for Labeled Contractibility with running time |V(H)|^{𝒪(|V(G)|)}, and show that this running time is optimal under {ETH}.
Cite as

Yashaswini Mathur and Prafullkumar Tale. A Finer View of the Parameterized Landscape of Labeled Graph Contractions. 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. 43:1-43:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mathur_et_al:LIPIcs.FSTTCS.2025.43,
  author =	{Mathur, Yashaswini and Tale, Prafullkumar},
  title =	{{A Finer View of the Parameterized Landscape of Labeled Graph Contractions}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{43:1--43:19},
  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.2025.43},
  URN =		{urn:nbn:de:0030-drops-251237},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.43},
  annote =	{Keywords: Labeled Contraction, ETH Lower-bound, Treewidth, NP-hard}
}
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.ESA.2025.103
On the Satisfiability of Random 3-SAT Formulas with k-Wise Independent Clauses

Authors: Ioannis Caragiannis, Nick Gravin, and Zhile Jiang

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

Abstract
The problem of identifying the satisfiability threshold of random 3-SAT formulas has received a lot of attention during the last decades and has inspired the study of other threshold phenomena in random combinatorial structures. The classical assumption in this line of research is that, for a given set of n Boolean variables, each clause is drawn uniformly at random among all sets of three literals from these variables, independently from other clauses. Here, we keep the uniform distribution of each clause, but deviate significantly from the independence assumption and consider richer families of probability distributions. For integer parameters n, m, and k, we denote by ℱ_k(n,m) the family of probability distributions that produce formulas with m clauses, each selected uniformly at random from all sets of three literals from the n variables, so that the clauses are k-wise independent. Our aim is to make general statements about the satisfiability or unsatisfiability of formulas produced by distributions in ℱ_k(n,m) for different values of the parameters n, m, and k. Our technical results are as follows: First, all probability distributions in ℱ₂(n,m) with m ∈ Ω(n³) return unsatisfiable formulas with high probability. This result is tight. We show that there exists a probability distribution 𝒟 ∈ ℱ₃(n,m) with m ∈ O(n³) so that a random formula drawn from 𝒟 is almost always satisfiable. In contrast, for m ∈ Ω(n²), any probability distribution 𝒟 ∈ ℱ₄(n,m) returns an unsatisfiable formula with high probability. This is our most surprising and technically involved result. Finally, for any integer k ≥ 2, any probability distribution 𝒟 ∈ ℱ_k(n,m) with m ∈ O(n^{1-1/k}) returns a satisfiable formula with high probability.
Cite as

Ioannis Caragiannis, Nick Gravin, and Zhile Jiang. On the Satisfiability of Random 3-SAT Formulas with k-Wise Independent Clauses. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 103:1-103:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{caragiannis_et_al:LIPIcs.ESA.2025.103,
  author =	{Caragiannis, Ioannis and Gravin, Nick and Jiang, Zhile},
  title =	{{On the Satisfiability of Random 3-SAT Formulas with k-Wise Independent Clauses}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{103:1--103:17},
  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.2025.103},
  URN =		{urn:nbn:de:0030-drops-245721},
  doi =		{10.4230/LIPIcs.ESA.2025.103},
  annote =	{Keywords: Random 3-SAT, k-wise independence, Random bipartite graph}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.13
Tight Bounds for Some Classical Problems Parameterized by Cutwidth

Authors: Narek Bojikian, Vera Chekan, and Stefan Kratsch

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

Abstract
Cutwidth is a widely studied parameter and it quantifies how well a graph can be decomposed along small edge-cuts. It complements pathwidth, which captures decomposition by small vertex separators, and it is well-known that cutwidth upper-bounds pathwidth. The SETH-tight parameterized complexity of problems on graphs of bounded pathwidth (and treewidth) has been actively studied over the past decade while for cutwidth the complexity of many classical problems remained open. For Hamiltonian Cycle, it is known that a (2+√2)^{pw} n^𝒪(1) algorithm is optimal for pathwidth under SETH [Cygan et al. JACM 2018]. Van Geffen et al. [J. Graph Algorithms Appl. 2020] and Bojikian et al. [STACS 2023] asked which running time is optimal for this problem parameterized by cutwidth. We answer this question with (1+√2)^{ctw} n^𝒪(1) by providing matching upper and lower bounds. Second, as our main technical contribution, we close the gap left by van Heck [2018] for Partition Into Triangles (and Triangle Packing) by improving both upper and lower bound and getting a tight bound of ∛{3}^{ctw} n^𝒪(1), which to our knowledge exhibits the only known tight non-integral basis apart from Hamiltonian Cycle [Cygan et al. JACM 2018] and C₄-Hitting Set [SODA 2025]. We show that the cuts inducing a disjoint union of paths of length three (unions of so-called Z-cuts) lie at the core of the complexity of the problem - usually lower-bound constructions use simpler cuts inducing either a matching or a disjoint union of bicliques. Finally, we determine the optimal running times for Max Cut (2^{ctw} n^𝒪(1)) and Induced Matching (3^{ctw} n^𝒪(1)) by providing matching lower bounds for the existing algorithms - the latter result also answers an open question for treewidth by Chaudhary and Zehavi [WG 2023].
Cite as

Narek Bojikian, Vera Chekan, and Stefan Kratsch. Tight Bounds for Some Classical Problems Parameterized by Cutwidth. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bojikian_et_al:LIPIcs.ESA.2025.13,
  author =	{Bojikian, Narek and Chekan, Vera and Kratsch, Stefan},
  title =	{{Tight Bounds for Some Classical Problems Parameterized by Cutwidth}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{13:1--13:17},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-244815},
  doi =		{10.4230/LIPIcs.ESA.2025.13},
  annote =	{Keywords: Parameterized complexity, cutwidth, Hamiltonian cycle, triangle packing, max cut, induced matching}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.41
Residue Domination in Bounded-Treewidth Graphs

Authors: Jakob Greilhuber, Philipp Schepper, and Philip Wellnitz

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

Abstract
For the vertex selection problem (σ,ρ)-DomSet one is given two fixed sets σ and ρ of integers and the task is to decide whether we can select vertices of the input graph such that, for every selected vertex, the number of selected neighbors is in σ and, for every unselected vertex, the number of selected neighbors is in ρ [Telle, Nord. J. Comp. 1994]. This framework covers many fundamental graph problems such as Independent Set and Dominating Set. We significantly extend the recent result by Focke et al. [SODA 2023] to investigate the case when σ and ρ are two (potentially different) residue classes modulo m ≥ 2. We study the problem parameterized by treewidth and present an algorithm that solves in time m^tw ⋅ n^O(1) the decision, minimization and maximization version of the problem. This significantly improves upon the known algorithms where for the case m ≥ 3 not even an explicit running time is known. We complement our algorithm by providing matching lower bounds which state that there is no (m-ε)^pw ⋅ n^O(1)-time algorithm parameterized by pathwidth pw, unless SETH fails. For m = 2, we extend these bounds to the minimization version as the decision version is efficiently solvable.
Cite as

Jakob Greilhuber, Philipp Schepper, and Philip Wellnitz. Residue Domination in Bounded-Treewidth Graphs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 41:1-41:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{greilhuber_et_al:LIPIcs.STACS.2025.41,
  author =	{Greilhuber, Jakob and Schepper, Philipp and Wellnitz, Philip},
  title =	{{Residue Domination in Bounded-Treewidth Graphs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{41:1--41:20},
  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.2025.41},
  URN =		{urn:nbn:de:0030-drops-228675},
  doi =		{10.4230/LIPIcs.STACS.2025.41},
  annote =	{Keywords: Parameterized Complexity, Treewidth, Generalized Dominating Set, Strong Exponential Time Hypothesis}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.44
Independence and Domination on Bounded-Treewidth Graphs: Integer, Rational, and Irrational Distances

Authors: Tim A. Hartmann and Dániel Marx

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

Abstract
The distance-d variants of Independent Set and Dominating Set problems have been extensively studied from different algorithmic viewpoints. In particular, the complexity of these problems are well understood on bounded-treewidth graphs [Katsikarelis, Lampis, and Paschos, Discret. Appl. Math 2022][Borradaile and Le, IPEC 2016]: given a tree decomposition of width t, the two problems can be solved in time d^t⋅ n^O(1) and (2d+1)^t⋅ n^O(1), respectively. Furthermore, assuming the Strong Exponential-Time Hypothesis (SETH), the base constants are best possible in these running times: they cannot be improved to d-ε and 2d+1-ε, respectively, for any ε > 0. We investigate continuous versions of these problems in a setting introduced by Megiddo and Tamir [SICOMP 1983], where every edge is modeled by a unit-length interval of points. In the δ-Dispersion problem, the task is to find a maximum number of points (possibly inside edges) that are pairwise at distance at least δ from each other. Similarly, in the δ-Covering problem, the task is to find a minimum number of points (possibly inside edges) such that every point of the graph (including those inside edges) is at distance at most δ from the selected point set. We provide a comprehensive understanding of these two problems on bounded-treewidth graphs. 1) Let δ = a/b with a and b being coprime. If a ≤ 2, then δ-Dispersion is polynomial-time solvable. For a ≥ 3, given a tree decomposition of width t, the problem can be solved in time (2a)^t⋅ n^O(1), and, assuming SETH, there is no (2a-ε)^t⋅n^{O(1)} time algorithm for any ε > 0. 2) Let δ = a/b with a and b being coprime. If a = 1, then δ-Covering is polynomial-time solvable. For a ≥ 2, given a tree decomposition of width t, the problem can be solved in time ((2+2(bod 2)) a)^t⋅ n^O(1), and, assuming SETH, there is no ((2+2(bod 2))a -ε)^t⋅n^O(1) time algorithm for any ε > 0. 3) For every fixed irrational number δ > 0 satisfying some mild computability condition, both δ-Dispersion and δ-Covering can be solved in time n^O(t) on graphs of treewidth t. We show a very explicitly defined irrational number δ = (4∑_{j=1}^∞ 2^{-2^j})^{-1} ≈ 0.790085 such that δ-Dispersion and δ/2-Covering are W[1]-hard parameterized by the treewidth t of the input graph, and, assuming ETH, cannot be solved in time f(t)⋅n^o(t). As a key step in obtaining these results, we extend earlier results on distance-d versions of Independent Set and Dominating Set: We determine the exact complexity of these problems in the special case when the input graph arises from some graph G' by subdividing every edge exactly b times.
Cite as

Tim A. Hartmann and Dániel Marx. Independence and Domination on Bounded-Treewidth Graphs: Integer, Rational, and Irrational Distances. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 44:1-44:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hartmann_et_al:LIPIcs.STACS.2025.44,
  author =	{Hartmann, Tim A. and Marx, D\'{a}niel},
  title =	{{Independence and Domination on Bounded-Treewidth Graphs: Integer, Rational, and Irrational Distances}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{44:1--44:19},
  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.2025.44},
  URN =		{urn:nbn:de:0030-drops-228700},
  doi =		{10.4230/LIPIcs.STACS.2025.44},
  annote =	{Keywords: Independence, Domination, Irrationals, Treewidth, SETH}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2016.27
Cut and Count and Representative Sets on Branch Decompositions

Authors: Willem J. A. Pino, Hans L. Bodlaender, and Johan M. M. van Rooij

Published in: LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)

Abstract
Recently, new techniques have been introduced to speed up dynamic programming algorithms on tree decompositions for connectivity problems: the 'Cut and Count' method and a method called the rank-based approach, based on representative sets and Gaussian elimination. These methods respectively give randomised and deterministic algorithms that are single exponential in the treewidth, and polynomial, respectively linear in the number of vertices. In this paper, we adapt these methods to branch decompositions yielding algorithms, both randomised and deterministic, that are in many cases faster than when tree decompositions would be used. In particular, we obtain the currently fastest randomised algorithms for several problems on planar graphs. When the involved weights are O(n^{O(1)}), we obtain faster randomised algorithms on planar graphs for Steiner Tree, Connected Dominating Set, Feedback Vertex Set and TSP, and a faster deterministic algorithm for TSP. When considering planar graphs with arbitrary real weights, we obtain faster deterministic algorithms for all four mentioned problems.
Cite as

Willem J. A. Pino, Hans L. Bodlaender, and Johan M. M. van Rooij. Cut and Count and Representative Sets on Branch Decompositions. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 27:1-27:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{pino_et_al:LIPIcs.IPEC.2016.27,
  author =	{Pino, Willem J. A. and Bodlaender, Hans L. and van Rooij, Johan M. M.},
  title =	{{Cut and Count and Representative Sets on Branch Decompositions}},
  booktitle =	{11th International Symposium on Parameterized and Exact Computation (IPEC 2016)},
  pages =	{27:1--27:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-023-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{63},
  editor =	{Guo, Jiong and Hermelin, Danny},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016.27},
  URN =		{urn:nbn:de:0030-drops-69450},
  doi =		{10.4230/LIPIcs.IPEC.2016.27},
  annote =	{Keywords: Graph algorithms, Branchwidth, Treewidth, Dynamic Programming, Planar Graphs}
}
Document
DOI: 10.4230/LIPIcs.STACS.2008.1329
Design by Measure and Conquer, A Faster Exact Algorithm for Dominating Set

Authors: Johan M. M. van Rooij and Hans L. Bodlaender

Published in: LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)

Abstract
The measure and conquer approach has proven to be a powerful tool to analyse exact algorithms for combinatorial problems, like Dominating Set and Independent Set. In this paper, we propose to use measure and conquer also as a tool in the design of algorithms. In an iterative process, we can obtain a series of branch and reduce algorithms. A mathematical analysis of an algorithm in the series with measure and conquer results in a quasiconvex programming problem. The solution by computer to this problem not only gives a bound on the running time, but also can give a new reduction rule, thus giving a new, possibly faster algorithm. This makes design by measure and conquer a form of computer aided algorithm design. When we apply the methodology to a Set Cover modelling of the Dominating Set problem, we obtain the currently fastest known exact algorithms for Dominating Set: an algorithm that uses $O(1.5134^n)$ time and polynomial space, and an algorithm that uses $O(1.5063^n)$ time.
Cite as

Johan M. M. van Rooij and Hans L. Bodlaender. Design by Measure and Conquer, A Faster Exact Algorithm for Dominating Set. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 657-668, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{vanrooij_et_al:LIPIcs.STACS.2008.1329,
  author =	{van Rooij, Johan M. M. and Bodlaender, Hans L.},
  title =	{{Design by Measure and Conquer, A Faster Exact Algorithm for Dominating Set}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{657--668},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Albers, Susanne and Weil, Pascal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1329},
  URN =		{urn:nbn:de:0030-drops-13297},
  doi =		{10.4230/LIPIcs.STACS.2008.1329},
  annote =	{Keywords: Exact algorithms, exponential time algorithms, branch and reduce, measure and conquer, dominating set, computer aided algorithm design}
}
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