11 Search Results for "Dregi, Markus"

Document
DOI: 10.4230/LIPIcs.STACS.2026.42
Computing Twin-Width via Treedepth and Vertex Integrity

Authors: Robert Ganian and Mathis Rocton

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

Abstract
Twin-width is a graph parameter that has become central to explaining the fixed-parameter tractability of first-order model checking across many graph classes. Despite its algorithmic importance, computing twin-width remains poorly understood: even recognizing graphs of twin-width at most four is NP-hard, and no fixed-parameter approximations parameterized by twin-width itself are known. A recent approach towards breaking this barrier focuses on first developing fixed-parameter algorithms for computing or approximating twin-width under parameterizations distinct from twin-width. Our first result establishes that approximating twin-width is fixed-parameter tractable when parameterized by treedepth, thereby breaking the long-standing barrier that all previous tractable parameterizations were based on deletion distance. The proof proceeds via oriented twin-width, yielding the first constructive evidence that this variant may be easier to handle algorithmically. As our second main result, we show that computing twin-width exactly is fixed-parameter tractable with respect to vertex integrity. This constitutes the first non-trivial parameterized algorithm for computing optimal contraction sequences.
Cite as

Robert Ganian and Mathis Rocton. Computing Twin-Width via Treedepth and Vertex Integrity. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 42:1-42:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{ganian_et_al:LIPIcs.STACS.2026.42,
  author =	{Ganian, Robert and Rocton, Mathis},
  title =	{{Computing Twin-Width via Treedepth and Vertex Integrity}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{42:1--42:20},
  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.2026.42},
  URN =		{urn:nbn:de:0030-drops-255318},
  doi =		{10.4230/LIPIcs.STACS.2026.42},
  annote =	{Keywords: twin-width, fixed-parameter algorithms, treedepth, vertex integrity}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.3
Parameterized Maximum Node-Disjoint Paths

Authors: Michael Lampis and Manolis Vasilakis

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

Abstract
We revisit the Maximum Node-Disjoint Paths problem, the natural optimization version of the famous Node-Disjoint Paths problem, where we are given an undirected graph G, k (demand) pairs of vertices (s_i, t_i), and an integer 𝓁, and are asked whether there exist at least 𝓁 vertex-disjoint paths in G whose endpoints are given pairs. This problem has been intensely studied from both the approximation and parameterized complexity point of view and is notably known to be intractable by standard structural parameters, such as tree-depth, as well as the combined parameter 𝓁 plus pathwidth. We present several results improving and clarifying this state of the art, with an emphasis towards FPT approximation. Our main positive contribution is to show that the problem’s intractability can be overcome using approximation: We show that for several of the structural parameters for which the problem is hard, most notably tree-depth, the problem admits an efficient FPT approximation scheme, returning a (1-ε)-approximate solution in time f(td,ε)n^𝒪(1). We manage to obtain these results by comprehensively mapping out the structural parameters for which the problem is FPT if 𝓁 is also a parameter, hence showing that understanding 𝓁 as a parameter is key to the problem’s approximability. This, in turn, is a problem we are able to solve via a surprisingly simple color-coding algorithm, which relies on identifying an insightful problem-specific variant of the natural parameter, namely the number of vertices used in the solution. The results above are quite encouraging, as they indicate that in some situations where the problem does not admit an FPT algorithm, it is still solvable almost to optimality in FPT time. A natural question is whether the FPT approximation algorithm we devised for tree-depth can be extended to pathwidth. We resolve this negatively, showing that under the Parameterized Inapproximability Hypothesis no FPT approximation scheme for this parameter is possible, even in time f(pw,ε)n^g(ε). We thus precisely determine the parameter border where the problem transitions from "hard but approximable" to "inapproximable". Lastly, we strengthen existing lower bounds by replacing W[1]-hardness by XNLP-completeness for parameter pathwidth, and improving the n^o(√{td}) ETH-based lower bound for tree-depth to (the optimal) n^o(td).
Cite as

Michael Lampis and Manolis Vasilakis. Parameterized Maximum Node-Disjoint Paths. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{lampis_et_al:LIPIcs.IPEC.2025.3,
  author =	{Lampis, Michael and Vasilakis, Manolis},
  title =	{{Parameterized Maximum Node-Disjoint Paths}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{3:1--3:15},
  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.2025.3},
  URN =		{urn:nbn:de:0030-drops-251357},
  doi =		{10.4230/LIPIcs.IPEC.2025.3},
  annote =	{Keywords: ETH, Maximum Node-Disjoint Paths, Parameterized Complexity, PIH}
}
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)

Copy BibTex To Clipboard

@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.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)

Copy BibTex To Clipboard

@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.ISAAC.2025.15
Parameterized Complexity of Directed Traveling Salesman Problem

Authors: Václav Blažej, Andreas Emil Feldmann, Foivos Fioravantes, Paweł Rzążewski, and Ondřej Suchý

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

Abstract
The Directed Traveling Salesman Problem (DTSP) is a variant of the classical Traveling Salesman Problem in which the edges in the graph are directed and a vertex and edge can be visited multiple times. The goal is to find a directed closed walk of minimum length (or total weight) that visits every vertex of the given graph at least once. In a yet more general version, Directed Waypoint Routing Problem (DWRP), some vertices are marked as terminals and we are only required to visit all terminals. Furthermore, each edge has its capacity bounding the number of times this edge can be used by a solution. While both problems (and many other variants of TSP) were extensively investigated, mostly from the approximation point of view, there are surprisingly few results concerning the parameterized complexity. Our starting point is the result of Marx et al. [APPROX/RANDOM 2016] who proved that DTSP is W[1]-hard parameterized by distance to pathwidth 3. In this paper we aim to initiate the systematic complexity study of variants of Directed Traveling Salesman Problem with respect to various, mostly structural, parameters. We show that DWRP is FPT parameterized by the solution size, the feedback edge number and the vertex integrity of the underlying undirected graph. Furthermore, the problem is XP parameterized by treewidth. On the complexity side, we show that the problem is W[1]-hard parameterized by the distance to constant treedepth.
Cite as

Václav Blažej, Andreas Emil Feldmann, Foivos Fioravantes, Paweł Rzążewski, and Ondřej Suchý. Parameterized Complexity of Directed Traveling Salesman Problem. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{blazej_et_al:LIPIcs.ISAAC.2025.15,
  author =	{Bla\v{z}ej, V\'{a}clav and Feldmann, Andreas Emil and Fioravantes, Foivos and Rz\k{a}\.{z}ewski, Pawe{\l} and Such\'{y}, Ond\v{r}ej},
  title =	{{Parameterized Complexity of Directed Traveling Salesman Problem}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{15:1--15:18},
  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.2025.15},
  URN =		{urn:nbn:de:0030-drops-249231},
  doi =		{10.4230/LIPIcs.ISAAC.2025.15},
  annote =	{Keywords: Directed TSP, parameterized complexity, vertex integrity, treedepth}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.29
The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration

Authors: Nicolas Bousquet, Quentin Deschamps, Arnaud Mary, Amer E. Mouawad, and Théo Pierron

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

Abstract
A dominating set of a graph G = (V,E) is a set of vertices D ⊆ V whose closed neighborhood is V, i.e., N[D] = V. We view a dominating set as a collection of tokens placed on the vertices of D. In the token sliding variant of the Dominating Set Reconfiguration problem (TS-DSR), we seek to transform a source dominating set into a target dominating set in G by sliding tokens along edges, and while maintaining a dominating set all along the transformation. TS-DSR is known to be PSPACE-complete even restricted to graphs of pathwidth w, for some non-explicit constant w and to be XL-complete parameterized by the size k of the solution. The first contribution of this article consists in using a novel approach to provide the first explicit constant for which the TS-DSR problem is PSPACE-complete, a question that was left open in the literature. From a parameterized complexity perspective, the token jumping variant of DSR, i.e., where tokens can jump to arbitrary vertices, is known to be FPT when parameterized by the size of the dominating sets on nowhere dense classes of graphs. But, in contrast, no non-trivial result was known about TS-DSR. We prove that DSR is actually much harder in the sliding model since it is XL-complete when restricted to bounded pathwidth graphs and even when parameterized by k plus the feedback vertex set number of the graph. This gives, for the first time, a difference of behavior between the complexity under token sliding and token jumping for some problem on graphs of bounded treewidth. All our results are obtained using a brand new method, based on the hardness of the so-called Tape Reconfiguration problem, a problem we believe to be of independent interest. We complement these hardness results with a positive result showing that DSR (parameterized by k) in the sliding model is FPT on planar graphs, also answering an open problem from the literature.
Cite as

Nicolas Bousquet, Quentin Deschamps, Arnaud Mary, Amer E. Mouawad, and Théo Pierron. The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bousquet_et_al:LIPIcs.ESA.2025.29,
  author =	{Bousquet, Nicolas and Deschamps, Quentin and Mary, Arnaud and Mouawad, Amer E. and Pierron, Th\'{e}o},
  title =	{{The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{29:1--29:15},
  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.2025.29},
  URN =		{urn:nbn:de:0030-drops-244974},
  doi =		{10.4230/LIPIcs.ESA.2025.29},
  annote =	{Keywords: combinatorial reconfiguration, parameterized complexity, structural graph parameters, treewidth, dominating set}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.15
Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms

Authors: Thomas Depian, Simon D. Fink, Robert Ganian, and Vaishali Surianarayanan

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

Abstract
In spite of the extensive study of stack and queue layouts, many fundamental questions remain open concerning the complexity-theoretic frontiers for computing stack and queue layouts. A stack (resp. queue) layout places vertices along a line and assigns edges to pages so that no two edges on the same page are crossing (resp. nested). We provide three new algorithms which together substantially expand our understanding of these problems: 1) A fixed-parameter algorithm for computing minimum-page stack and queue layouts w.r.t. the vertex integrity of an n-vertex graph G. This result is motivated by an open question in the literature and generalizes the previous algorithms parameterizing by the vertex cover number of G. The proof relies on a newly developed Ramsey pruning technique. Vertex integrity intuitively measures the vertex deletion distance to a subgraph with only small connected components. 2) An n^𝒪(q 𝓁) algorithm for computing 𝓁-page stack and queue layouts of page width at most q. This is the first algorithm avoiding a double-exponential dependency on the parameters. The page width of a layout measures the maximum number of edges one needs to cross on any page to reach the outer face. 3) A 2^𝒪(n) algorithm for computing 1-page queue layouts. This improves upon the previously fastest n^𝒪(n) algorithm and can be seen as a counterpart to the recent subexponential algorithm for computing 2-page stack layouts [ICALP'24], but relies on an entirely different technique.
Cite as

Thomas Depian, Simon D. Fink, Robert Ganian, and Vaishali Surianarayanan. Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{depian_et_al:LIPIcs.ESA.2025.15,
  author =	{Depian, Thomas and Fink, Simon D. and Ganian, Robert and Surianarayanan, Vaishali},
  title =	{{Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{15:1--15:18},
  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.2025.15},
  URN =		{urn:nbn:de:0030-drops-244835},
  doi =		{10.4230/LIPIcs.ESA.2025.15},
  annote =	{Keywords: stack layouts, queue layouts, parameterized algorithms, vertex integrity, Ramsey theory}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.116
Fast Gaussian Elimination for Low Treewidth Matrices

Authors: Martin Fürer, Carlos Hoppen, and Vilmar Trevisan

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

Abstract
Let A = (a_{ij}) be an m× n matrix whose elements lie in an arbitrary field 𝔽, and let G be the bipartite graph with vertex set {v_1,…,v_m} ∪ {w_1,…,w_n} such that vertices v_i and w_j are adjacent if and only if a_{ij} ≠ 0. We introduce an algorithm that finds an m× n matrix U in row echelon form and a permutation matrix Q of order n, such that AQ is row equivalent to U. If a tree decomposition 𝒯 of G of width k and size O(k(m+n)) is part of the input, then Q and the columns of U that contain a pivot can be computed in time O(k²(m+n)). Among other things, this allows us to compute the rank and the determinant of A in time O(k²(m+n)). It also allows us to decide in time O(k²(m+n)) whether the linear system Ax = b has a solution and to compute a solution of the linear system in case it exists.
Cite as

Martin Fürer, Carlos Hoppen, and Vilmar Trevisan. Fast Gaussian Elimination for Low Treewidth Matrices. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 116:1-116:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{furer_et_al:LIPIcs.ESA.2025.116,
  author =	{F\"{u}rer, Martin and Hoppen, Carlos and Trevisan, Vilmar},
  title =	{{Fast Gaussian Elimination for Low Treewidth Matrices}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{116:1--116:15},
  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.2025.116},
  URN =		{urn:nbn:de:0030-drops-245855},
  doi =		{10.4230/LIPIcs.ESA.2025.116},
  annote =	{Keywords: Gaussian elimination, FPT algorithms, treewidth}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.42
Broadcasting Under Structural Restrictions

Authors: Yudai Egami, Tatsuya Gima, Tesshu Hanaka, Yasuaki Kobayashi, 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 the Telephone Broadcast problem we are given a graph G = (V,E) with a designated source vertex s ∈ V. Our goal is to transmit a message, which is initially known only to s, to all vertices of the graph by using a process where in each round an informed vertex may transmit the message to one of its uninformed neighbors. The optimization objective is to minimize the number of rounds. Following up on several recent works, we investigate the structurally parameterized complexity of Telephone Broadcast. In particular, we first strengthen existing NP-hardness results by showing that the problem remains NP-complete on graphs of bounded tree-depth and also on cactus graphs which are one vertex deletion away from being path forests. Motivated by this (severe) hardness, we study several other parameterizations of the problem and obtain FPT algorithms parameterized by vertex integrity (generalizing a recent FPT algorithm parameterized by vertex cover by Fomin, Fraigniaud, and Golovach [TCS 2024]) and by distance to clique, as well as FPT approximation algorithms parameterized by clique-cover and cluster vertex deletion. Furthermore, we obtain structural results that relate the length of the optimal broadcast protocol of a graph G with its pathwidth and tree-depth. By presenting a substantial improvement over the best previously known bound for pathwidth (Aminian, Kamali, Seyed-Javadi, and Sumedha [ICALP 2025]) we exponentially improve the approximation ratio achievable in polynomial time on graphs of bounded pathwidth from 𝒪(4^pw) to 𝒪(pw).
Cite as

Yudai Egami, Tatsuya Gima, Tesshu Hanaka, Yasuaki Kobayashi, Michael Lampis, Valia Mitsou, Edouard Nemery, Yota Otachi, Manolis Vasilakis, and Daniel Vaz. Broadcasting Under Structural Restrictions. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 42:1-42:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{egami_et_al:LIPIcs.MFCS.2025.42,
  author =	{Egami, Yudai and Gima, Tatsuya and Hanaka, Tesshu and Kobayashi, Yasuaki and Lampis, Michael and Mitsou, Valia and Nemery, Edouard and Otachi, Yota and Vasilakis, Manolis and Vaz, Daniel},
  title =	{{Broadcasting Under Structural Restrictions}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{42:1--42:18},
  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.2025.42},
  URN =		{urn:nbn:de:0030-drops-241492},
  doi =		{10.4230/LIPIcs.MFCS.2025.42},
  annote =	{Keywords: Parameterized Complexity, Structural Graph Parameters, Telephone Broadcast}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.120
Treewidth Parameterized by Feedback Vertex Number

Authors: Hendrik Molter, Meirav Zehavi, and Amit Zivan

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

Abstract
We provide the first algorithm for computing an optimal tree decomposition for a given graph G that runs in single exponential time in the feedback vertex number of G, that is, in time 2^{𝒪(fvn(G))}⋅ n^{𝒪(1)}, where fvn(G) is the feedback vertex number of G and n is the number of vertices of G. On a classification level, this improves the previously known results by Chapelle et al. [Discrete Applied Mathematics '17] and Fomin et al. [Algorithmica '18], who independently showed that an optimal tree decomposition can be computed in single exponential time in the vertex cover number of G. One of the biggest open problems in the area of parameterized complexity is whether we can compute an optimal tree decomposition in single exponential time in the treewidth of the input graph. The currently best known algorithm by Korhonen and Lokshtanov [STOC '23] runs in 2^{𝒪(tw(G)²)}⋅ n⁴ time, where tw(G) is the treewidth of G. Our algorithm improves upon this result on graphs G where fvn(G) ∈ o(tw(G)²). On a different note, since fvn(G) is an upper bound on tw(G), our algorithm can also be seen either as an important step towards a positive resolution of the above-mentioned open problem, or, if its answer is negative, then a mark of the tractability border of single exponential time algorithms for the computation of treewidth.
Cite as

Hendrik Molter, Meirav Zehavi, and Amit Zivan. Treewidth Parameterized by Feedback Vertex Number. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 120:1-120:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{molter_et_al:LIPIcs.ICALP.2025.120,
  author =	{Molter, Hendrik and Zehavi, Meirav and Zivan, Amit},
  title =	{{Treewidth Parameterized by Feedback Vertex Number}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{120:1--120:20},
  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.2025.120},
  URN =		{urn:nbn:de:0030-drops-234979},
  doi =		{10.4230/LIPIcs.ICALP.2025.120},
  annote =	{Keywords: Treewidth, Tree Decomposition, Exact Algorithms, Single Exponential Time, Feedback Vertex Number, Dynamic Programming}
}
Document
DOI: 10.4230/LIPIcs.STACS.2016.31
Kernelization and Sparseness: the Case of Dominating Set

Authors: Pål Grønås Drange, Markus Dregi, Fedor V. Fomin, Stephan Kreutzer, Daniel Lokshtanov, Marcin Pilipczuk, Michal Pilipczuk, Felix Reidl, Fernando Sánchez Villaamil, Saket Saurabh, Sebastian Siebertz, and Somnath Sikdar

Published in: LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)

Abstract
We prove that for every positive integer r and for every graph class G of bounded expansion, the r-DOMINATING SET problem admits a linear kernel on graphs from G. Moreover, in the more general case when G is only assumed to be nowhere dense, we give an almost linear kernel on G for the classic DOMINATING SET problem, i.e., for the case r=1. These results generalize a line of previous research on finding linear kernels for DOMINATING SET and r-DOMINATING SET (Alber et al., JACM 2004, Bodlaender et al., FOCS 2009, Fomin et al., SODA 2010, Fomin et al., SODA 2012, Fomin et al., STACS 2013). However, the approach taken in this work, which is based on the theory of sparse graphs, is radically different and conceptually much simpler than the previous approaches. We complement our findings by showing that for the closely related CONNECTED DOMINATING SET problem, the existence of such kernelization algorithms is unlikely, even though the problem is known to admit a linear kernel on H-topological-minor-free graphs (Fomin et al., STACS 2013). Also, we prove that for any somewhere dense class G, there is some r for which r-DOMINATING SET is W[2]-hard on G. Thus, our results fall short of proving a sharp dichotomy for the parameterized complexity of r-DOMINATING SET on subgraph-monotone graph classes: we conjecture that the border of tractability lies exactly between nowhere dense and somewhere dense graph classes.
Cite as

Pål Grønås Drange, Markus Dregi, Fedor V. Fomin, Stephan Kreutzer, Daniel Lokshtanov, Marcin Pilipczuk, Michal Pilipczuk, Felix Reidl, Fernando Sánchez Villaamil, Saket Saurabh, Sebastian Siebertz, and Somnath Sikdar. Kernelization and Sparseness: the Case of Dominating Set. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{drange_et_al:LIPIcs.STACS.2016.31,
  author =	{Drange, P\r{a}l Gr{\o}n\r{a}s and Dregi, Markus and Fomin, Fedor V. and Kreutzer, Stephan and Lokshtanov, Daniel and Pilipczuk, Marcin and Pilipczuk, Michal and Reidl, Felix and S\'{a}nchez Villaamil, Fernando and Saurabh, Saket and Siebertz, Sebastian and Sikdar, Somnath},
  title =	{{Kernelization and Sparseness: the Case of Dominating Set}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Ollinger, Nicolas and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.31},
  URN =		{urn:nbn:de:0030-drops-57327},
  doi =		{10.4230/LIPIcs.STACS.2016.31},
  annote =	{Keywords: kernelization, dominating set, bounded expansion, nowhere dense}
}
  • Refine by Type
  • 11 Document/PDF
  • 10 Document/HTML

  • Refine by Publication Year
  • 1 2026
  • 9 2025
  • 1 2016

  • Refine by Author
  • 2 Ganian, Robert
  • 2 Gima, Tatsuya
  • 2 Kobayashi, Yasuaki
  • 2 Lampis, Michael
  • 2 Otachi, Yota
  • Show More...

  • Refine by Series/Journal
  • 11 LIPIcs

  • Refine by Classification
  • 8 Theory of computation → Parameterized complexity and exact algorithms
  • 1 Mathematics of computing → Combinatorics
  • 1 Mathematics of computing → Graph algorithms
  • 1 Theory of computation → Design and analysis of algorithms
  • 1 Theory of computation → Finite Model Theory
  • Show More...

  • Refine by Keyword
  • 3 vertex integrity
  • 2 Parameterized Complexity
  • 2 Treewidth
  • 2 dominating set
  • 2 parameterized complexity
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact