37 Search Results for "Nichterlein, André"

Document
DOI: 10.4230/LIPIcs.FUN.2026.29
Finding Shortest Walks in Kuru Kuru Kururin

Authors: Mickaël Laurent and Maher Mallem

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
This paper serves as a celebration of the twenty-fifth anniversary of Kuru Kuru Kururin. Although this video game is presented as a collection of two-dimensional puzzles based on rotation, it naturally invites players to complete its levels as quickly as possible. This has led to a surprisingly rich and challenging playing field to finding foremost temporal walks. In this work, we tackle this problem both in theory and in practice. First, we introduce a model for the game and provide an in-depth complexity analysis. Most notably, we show how each gameplay mechanic independently brings a layer of NP-hardness and/or co-NP-hardness. We also provide a pseudo-polynomial time algorithm for the general problem and identify several cases which can be solved in polynomial time. Along the way, we discuss connections to the more established framework of temporal graphs, both in the point model and the interval model. Then, we propose simple and flexible algorithmic techniques to reduce state space and guide the search, offering trade-offs between precision and computation speed in practice. These techniques were implemented and tested using a full recreation of the game physics and the levels from the original game. We demonstrate the efficiency of our framework in several settings - with or without taking damage, with or without unintended game mechanics - and relate empirical struggles which we encountered in practice to our complexity analysis. Our implementation is open source and fully available online, offering a novel and amusing setting to benchmark shortest path algorithms.
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Mickaël Laurent and Maher Mallem. Finding Shortest Walks in Kuru Kuru Kururin. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{laurent_et_al:LIPIcs.FUN.2026.29,
  author =	{Laurent, Micka\"{e}l and Mallem, Maher},
  title =	{{Finding Shortest Walks in Kuru Kuru Kururin}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{29:1--29:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.29},
  URN =		{urn:nbn:de:0030-drops-257480},
  doi =		{10.4230/LIPIcs.FUN.2026.29},
  annote =	{Keywords: Shortest path, Complexity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.12
Density Matters: A Complexity Dichotomy of Deleting Edges to Bound Subgraph Density

Authors: Matthias Bentert, Tom-Lukas Breitkopf, Vincent Froese, Anton Herrmann, and André Nichterlein

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

Abstract
We study τ-Bounded-Density Edge Deletion (τ-BDED), where given an undirected graph G, the task is to remove as few edges as possible to obtain a graph G' where no subgraph of G' has density more than τ. The density of a (sub)graph is the number of edges divided by the number of vertices. This problem was recently introduced and shown to be NP-hard for τ ∈ {2/3, 3/4, 1 + 1/25}, but polynomial-time solvable for τ ∈ {0,1/2,1} [Bazgan et al., JCSS 2025]. We provide a complete dichotomy with respect to the target density τ: 1) If 2τ ∈ ℕ (half-integral target density) or τ < 2/3, then τ-BDED is polynomial-time solvable. 2) Otherwise, τ-BDED is NP-hard. We complement the NP-hardness with fixed-parameter tractability with respect to the treewidth of G. Moreover, for integral target density τ ∈ ℕ, we show τ-BDED to be solvable in randomized O(m^{1 + o(1)}) time. Our algorithmic results are based on a reduction to a new general flow problem on restricted networks that, depending on τ, can be solved via Maximum s-t-Flow or General Factors. We believe this connection between these variants of flow and matching to be of independent interest.
Cite as

Matthias Bentert, Tom-Lukas Breitkopf, Vincent Froese, Anton Herrmann, and André Nichterlein. Density Matters: A Complexity Dichotomy of Deleting Edges to Bound Subgraph Density. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bentert_et_al:LIPIcs.STACS.2026.12,
  author =	{Bentert, Matthias and Breitkopf, Tom-Lukas and Froese, Vincent and Herrmann, Anton and Nichterlein, Andr\'{e}},
  title =	{{Density Matters: A Complexity Dichotomy of Deleting Edges to Bound Subgraph Density}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{12:1--12:20},
  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.2026.12},
  URN =		{urn:nbn:de:0030-drops-255012},
  doi =		{10.4230/LIPIcs.STACS.2026.12},
  annote =	{Keywords: Transshipment, Maximum Flow, General Factors, Matching, Graph Modification Problem}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.10
A Polynomial Bound on the Pathwidth of Graphs Edge-Coverable by k Shortest Paths

Authors: Julien Baste, Lucas De Meyer, Ugo Giocanti, Etienne Objois, and Timothé Picavet

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

Abstract
Dumas, Foucaud, Perez and Todinca [SIAM J. Disc. Math., 2024] recently proved that every graph whose edge set can be covered by k shortest paths has pathwidth at most 3^k. In this paper, we improve this upper bound on the pathwidth to a polynomial bound; namely, we show that every graph whose edge set can be covered by k shortest paths has pathwidth O(k⁴), answering a question from the same paper. Moreover, we also prove that when k ≤ 3, every such graph has pathwidth at most k (and this bound is tight). Eventually, we show that even though there exist graphs with arbitrary large treewidth whose vertex set can be covered by 2 isometric trees, every graph whose set of edges can be covered by 2 isometric trees has treewidth at most 2.
Cite as

Julien Baste, Lucas De Meyer, Ugo Giocanti, Etienne Objois, and Timothé Picavet. A Polynomial Bound on the Pathwidth of Graphs Edge-Coverable by k Shortest Paths. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{baste_et_al:LIPIcs.STACS.2026.10,
  author =	{Baste, Julien and De Meyer, Lucas and Giocanti, Ugo and Objois, Etienne and Picavet, Timoth\'{e}},
  title =	{{A Polynomial Bound on the Pathwidth of Graphs Edge-Coverable by k Shortest Paths}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{10:1--10:17},
  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.2026.10},
  URN =		{urn:nbn:de:0030-drops-254999},
  doi =		{10.4230/LIPIcs.STACS.2026.10},
  annote =	{Keywords: Structural Graph Theory, Coverings, Metrics, Pathwidth, Treewdidth, Parameterized Algorithms, Layerings}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.39
Efficient Algorithms for the Disjoint Shortest Paths Problem and Its Extensions

Authors: Keerti Choudhary, Amit Kumar, and Lakshay Saggi

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We study the 2-Disjoint Shortest Paths (2-DSP) problem: given a directed weighted graph and two terminal pairs (s₁,t₁) and (s₂,t₂), decide whether there exist vertex-disjoint shortest paths between each pair. Building on recent advances in disjoint shortest paths for DAGs and undirected graphs (Akmal et al. 2024), we present an O(mn log n)-time algorithm for this problem in weighted directed graphs that do not contain negative or zero weight cycles. This algorithm presents a significant improvement over the previously known O(m⁵n)-time bound (Berczi et al. 2017). Our approach exploits the algebraic structure of polynomials that enumerate shortest paths between terminal pairs. A key insight is that these polynomials admit a recursive decomposition, enabling efficient evaluation via dynamic programming over fields of characteristic two. Furthermore, we demonstrate how to report the corresponding paths in O(mn² log n)-time. In addition, we extend our techniques to a more general setting: given two terminal pairs (s₁, t₁) and (s₂, t₂) in a directed graph, find the minimum possible number of vertex intersections between any shortest path from s₁ to t₁ and s₂ to t₂. We call this the Minimum 2-Disjoint Shortest Paths (Min-2-DSP) problem. We provide in this paper the first efficient algorithm for this problem, including an O(m² n³)-time algorithm for directed graphs with positive edge weights, and an O(m+n)-time algorithm for DAGs and undirected graphs. Moreover, if the number of intersecting vertices is at least one, we show that it is possible to report the paths in the same O(m+n)-time. This is somewhat surprising, as there is no known o(mn) time algorithm for explicitly reporting the paths if they are vertex-disjoint, and is left as an open problem in (Akmal et al. 2024).
Cite as

Keerti Choudhary, Amit Kumar, and Lakshay Saggi. Efficient Algorithms for the Disjoint Shortest Paths Problem and Its Extensions. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 39:1-39:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{choudhary_et_al:LIPIcs.ITCS.2026.39,
  author =	{Choudhary, Keerti and Kumar, Amit and Saggi, Lakshay},
  title =	{{Efficient Algorithms for the Disjoint Shortest Paths Problem and Its Extensions}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{39:1--39:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.39},
  URN =		{urn:nbn:de:0030-drops-253267},
  doi =		{10.4230/LIPIcs.ITCS.2026.39},
  annote =	{Keywords: Disjoint paths, Disjoint shortest paths, Algebraic graph algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.66
A Parameterized-Complexity Framework for Finding Local Optima

Authors: Robert Ganian, Hung P. Hoang, Christian Komusiewicz, and Nils Morawietz

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
Local search is a fundamental optimization technique that is both widely used in practice and deeply studied in theory, yet its computational complexity remains poorly understood. The traditional frameworks, PLS and the standard algorithm problem, introduced by Johnson, Papadimitriou, and Yannakakis (1988) fail to capture the methodology of local search algorithms: PLS is concerned with finding a local optimum and not with using local search, while the standard algorithm problem restricts each improvement step to follow a fixed pivoting rule. In this work, we introduce a novel formulation of local search which provides a middle ground between these models. In particular, the task is to output not only a local optimum but also a chain of local improvements leading to it. With this framework, we aim to capture the challenge in designing a good pivoting rule. Especially, when combined with the parameterized complexity paradigm, it enables both strong lower bounds and meaningful tractability results. Unlike previous works that combined parameterized complexity with local search, our framework targets the whole task of finding a local optimum and not only a single improvement step. Focusing on two representative meta-problems - Subset Weight Optimization Problem with the c-swap neighborhood and Weighted Circuit with the flip neighborhood - we establish fixed-parameter tractability results related to the number of distinct weights, while ruling out an analogous result when parameterizing by the distance to the nearest optimum via a new type of reduction.
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Robert Ganian, Hung P. Hoang, Christian Komusiewicz, and Nils Morawietz. A Parameterized-Complexity Framework for Finding Local Optima. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 66:1-66:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ganian_et_al:LIPIcs.ITCS.2026.66,
  author =	{Ganian, Robert and Hoang, Hung P. and Komusiewicz, Christian and Morawietz, Nils},
  title =	{{A Parameterized-Complexity Framework for Finding Local Optima}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{66:1--66:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.66},
  URN =		{urn:nbn:de:0030-drops-253532},
  doi =		{10.4230/LIPIcs.ITCS.2026.66},
  annote =	{Keywords: Local Search, Parameterized Complexity, PLS}
}
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
DOI: 10.4230/LIPIcs.IPEC.2025.16
Designing Compact ILPs via Fast Witness Verification

Authors: Michał Włodarczyk

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

Abstract
The standard formalization of preprocessing in parameterized complexity is given by kernelization. In this work, we depart from this paradigm and study a different type of preprocessing for problems without polynomial kernels, still aiming at producing instances that are easily solvable in practice. Specifically, we ask for which parameterized problems an instance (I,k) can be reduced in polynomial time to an integer linear program (ILP) with poly(k) constraints. We show that this property coincides with the parameterized complexity class WK[1], previously studied in the context of Turing kernelization lower bounds. In turn, the class WK[1] enjoys an elegant characterization in terms of witness verification protocols: a yes-instance should admit a witness of size poly(k) that can be verified in time poly(k). By combining known data structures with new ideas, we design such protocols for several problems, such as r-Way Cut, Vertex Multiway Cut, Steiner Tree, and Minimum Common String Partition, thus showing that they can be modeled by compact ILPs. We also present explicit ILP and MILP formulations for Weighted Vertex Cover on graphs with small (unweighted) vertex cover number. We believe that these results will provide a background for a systematic study of ILP-oriented preprocessing procedures for parameterized problems.
Cite as

Michał Włodarczyk. Designing Compact ILPs via Fast Witness Verification. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{wlodarczyk:LIPIcs.IPEC.2025.16,
  author =	{W{\l}odarczyk, Micha{\l}},
  title =	{{Designing Compact ILPs via Fast Witness Verification}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{16:1--16:18},
  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.2025.16},
  URN =		{urn:nbn:de:0030-drops-251481},
  doi =		{10.4230/LIPIcs.IPEC.2025.16},
  annote =	{Keywords: integer programming, kernelization, nondeterminism, multiway cut}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.25
Structural Parameterizations of Simultaneous Planarity

Authors: Thomas Depian, Simon D. Fink, Alexander Firbas, Robert Ganian, Matthias Pfretzschner, and Ignaz Rutter

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

Abstract
Given a set of graphs on the same vertex set, the problem Simultaneous Embedding With Fixed Edges (SEFE) asks, whether there exist planar drawings of all input graphs, such that every pair of drawings coincides on their shared subgraph. It is known that SEFE is NP-complete [Elisabeth Gassner et al., 2006], even in the so-called sunflower case, where all pairs of input graphs have the same shared graph G_∩ [Marcus Schaefer, 2012]. Fink, Pfretzschner, and Rutter [Simon D. Fink et al., 2023] recently initiated the study of the parameterized complexity of SEFE in the sunflower case, mainly focusing on structural parameters of G_∩. In this work, we shift the focus towards parameters of the union graph G_∪ that contains the edges of all input graphs. On the positive side, we establish fixed-parameter tractability for the problem with respect to the feedback edge set number of G_∪. We complement this result by showing that it, surprisingly, remains NP-complete even if G_∪ has constant vertex cover number. These results settle two open questions posed by Fink et al. [Simon D. Fink et al., 2023].
Cite as

Thomas Depian, Simon D. Fink, Alexander Firbas, Robert Ganian, Matthias Pfretzschner, and Ignaz Rutter. Structural Parameterizations of Simultaneous Planarity. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{depian_et_al:LIPIcs.ISAAC.2025.25,
  author =	{Depian, Thomas and Fink, Simon D. and Firbas, Alexander and Ganian, Robert and Pfretzschner, Matthias and Rutter, Ignaz},
  title =	{{Structural Parameterizations of Simultaneous Planarity}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{25:1--25:17},
  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.2025.25},
  URN =		{urn:nbn:de:0030-drops-249332},
  doi =		{10.4230/LIPIcs.ISAAC.2025.25},
  annote =	{Keywords: SEFE, Simultaneous Planarity, Fixed-Parameter Tractability, NP-hardness}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.83
Fault-Tolerant Matroid Bases

Authors: Matthias Bentert, Fedor V. Fomin, Petr A. Golovach, and Laure Morelle

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

Abstract
We investigate the problem of constructing fault-tolerant bases in matroids. Given a matroid ℳ and a redundancy parameter k, a k-fault-tolerant basis is a minimum-size set of elements such that, even after the removal of any k elements, the remaining subset still spans the entire ground set. Since matroids generalize linear independence across structures such as vector spaces, graphs, and set systems, this problem unifies and extends several fault-tolerant concepts appearing in prior research. Our main contribution is a fixed-parameter tractable (FPT) algorithm for the k-fault-tolerant basis problem, parameterized by both k and the rank r of the matroid. This two-variable parameterization by k + r is shown to be tight in the following sense. On the one hand, the problem is already NP-hard for k = 1. On the other hand, it is Para-NP-hard for r ≥ 3 and polynomial-time solvable for r ≤ 2.
Cite as

Matthias Bentert, Fedor V. Fomin, Petr A. Golovach, and Laure Morelle. Fault-Tolerant Matroid Bases. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 83:1-83:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bentert_et_al:LIPIcs.ESA.2025.83,
  author =	{Bentert, Matthias and Fomin, Fedor V. and Golovach, Petr A. and Morelle, Laure},
  title =	{{Fault-Tolerant Matroid Bases}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{83:1--83:14},
  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.2025.83},
  URN =		{urn:nbn:de:0030-drops-245511},
  doi =		{10.4230/LIPIcs.ESA.2025.83},
  annote =	{Keywords: Parameterized Complexity, matroids, robust bases}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.32
Fantastic Flips and Where to Find Them: A General Framework for Parameterized Local Search on Partitioning Problems

Authors: Niels Grüttemeier, Nils Morawietz, and Frank Sommer

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

Abstract
Parameterized local search combines classic local search heuristics with the paradigm of parameterized algorithmics. While most local search algorithms aim to improve given solutions by performing one single operation on a given solution, the parameterized approach aims to improve a solution by performing k simultaneous operations. Herein, k is a parameter called search radius for which the value can be chosen by a user. One major goal in the field of parameterized local search is to outline the trade-off between the size of k and the running time of the local search step. In this work, we introduce an abstract framework that generalizes natural parameterized local search approaches for a large class of partitioning problems: Given n items that are partitioned into b bins and a target function that evaluates the quality of the current partition, one asks whether it is possible to improve the solution by removing up to k items from their current bins and reassigning them to other bins. Among others, our framework applies for the local search versions of problems like Cluster Editing, Vector Bin Packing, and Nash Social Welfare. Motivated by a real-world application of the problem Vector Bin Packing, we introduce a parameter called number of types τ ≤ n and show that all problems fitting in our framework can be solved in τ^k ⋅ 2^𝒪(k) ⋅ |I|^𝒪(1) time, where |I| denotes the total input size. In case of Cluster Editing, the parameter τ generalizes the well-known parameter neighborhood diversity of the input graph. We complement these algorithms by showing that for all considered problems, an algorithm significantly improving over our algorithm with running time τ^k ⋅ 2^𝒪(k) ⋅ |I|^𝒪(1) would contradict the Exponential Time Hypothesis. Additionally, we show that even on very restricted instances, all considered problems are W[1]-hard when parameterized by the search radius k alone. In case of the local search version of Vector Bin Packing, we provide an even stronger W[1]-hardness result.
Cite as

Niels Grüttemeier, Nils Morawietz, and Frank Sommer. Fantastic Flips and Where to Find Them: A General Framework for Parameterized Local Search on Partitioning Problems. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gruttemeier_et_al:LIPIcs.WADS.2025.32,
  author =	{Gr\"{u}ttemeier, Niels and Morawietz, Nils and Sommer, Frank},
  title =	{{Fantastic Flips and Where to Find Them: A General Framework for Parameterized Local Search on Partitioning Problems}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{32:1--32:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.32},
  URN =		{urn:nbn:de:0030-drops-242631},
  doi =		{10.4230/LIPIcs.WADS.2025.32},
  annote =	{Keywords: Flip-Neighborhood, Cluster Editing, Vector Bin Packing, Vertex Cover, NP-hard problem, Max c-Cut}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.90
Elimination Distance to Dominated Clusters

Authors: Nicole Schirrmacher, Sebastian Siebertz, and Alexandre Vigny

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

Abstract
In the Dominated Cluster Deletion problem, we are given an undirected graph G and integers k and d and the question is to decide whether there exists a set of at most k vertices whose removal results in a graph in which each connected component has a dominating set of size at most d. In the Elimination Distance to Dominated Clusters problem, we are again given an undirected graph G and integers k and d and the question is to decide whether we can recursively delete vertices up to depth k such that each remaining connected component has a dominating set of size at most d. Bentert et al. [Bentert et al., MFCS 2024] recently provided an almost complete classification of the parameterized complexity of Dominated Cluster Deletion with respect to the parameters k, d, c, and Δ, where c and Δ are the degeneracy, and the maximum degree of the input graph, respectively. In particular, they provided a non-uniform algorithm with running time f(k,d)⋅ n^{𝒪(d)}. They left as an open problem whether the problem is fixed-parameter tractable with respect to the parameter k + d + c. We provide a uniform algorithm running in time f(k,d)⋅ n^{𝒪(d)} for both Dominated Cluster Deletion and Elimination Distance to Dominated Clusters. We furthermore show that both problems are FPT when parameterized by k+d+𝓁, where 𝓁 is the semi-ladder index of the input graph, a parameter that is upper bounded and may be much smaller than the degeneracy c, positively answering the open question of Bentert et al. We further complete the picture by providing an almost full classification for the parameterized complexity and kernelization complexity of Elimination Distance to Dominated Clusters. The one difficult base case that remains open is whether Treedepth (the case d = 0) is NP-hard on graphs of bounded maximum degree.
Cite as

Nicole Schirrmacher, Sebastian Siebertz, and Alexandre Vigny. Elimination Distance to Dominated Clusters. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 90:1-90:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{schirrmacher_et_al:LIPIcs.MFCS.2025.90,
  author =	{Schirrmacher, Nicole and Siebertz, Sebastian and Vigny, Alexandre},
  title =	{{Elimination Distance to Dominated Clusters}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{90:1--90:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.90},
  URN =		{urn:nbn:de:0030-drops-241978},
  doi =		{10.4230/LIPIcs.MFCS.2025.90},
  annote =	{Keywords: Graph theory, Fixed-parameter algorithms, Dominated cluster, Elimination distance}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.65
Parameterized Spanning Tree Congestion

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

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

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

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

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@InProceedings{lampis_et_al:LIPIcs.MFCS.2025.65,
  author =	{Lampis, Michael and Mitsou, Valia and Nemery, Edouard and Otachi, Yota and Vasilakis, Manolis and Vaz, Daniel},
  title =	{{Parameterized Spanning Tree Congestion}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{65:1--65:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.65},
  URN =		{urn:nbn:de:0030-drops-241724},
  doi =		{10.4230/LIPIcs.MFCS.2025.65},
  annote =	{Keywords: Parameterized Complexity, Treewidth, Graph Width Parameters}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.22
Concurrent Iterated Local Search for the Maximum Weight Independent Set Problem

Authors: Ernestine Großmann, Kenneth Langedal, and Christian Schulz

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
The Maximum Weight Independent Set problem is a fundamental NP-hard problem in combinatorial optimization with several real-world applications. Given an undirected vertex-weighted graph, the problem is to find a subset of the vertices with the highest possible weight under the constraint that no two vertices in the set can share an edge. This work presents a new iterated local search heuristic called CHILS (Concurrent Hybrid Iterated Local Search). The implementation of CHILS is specifically designed to handle large graphs of varying densities. CHILS outperforms the current state-of-the-art on commonly used benchmark instances, especially on the largest instances. As an added benefit, CHILS can run in parallel to leverage the power of multicore processors. The general technique used in CHILS is a new concurrent metaheuristic called Concurrent Difference-Core Heuristic that can also be applied to other combinatorial problems.
Cite as

Ernestine Großmann, Kenneth Langedal, and Christian Schulz. Concurrent Iterated Local Search for the Maximum Weight Independent Set Problem. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gromann_et_al:LIPIcs.SEA.2025.22,
  author =	{Gro{\ss}mann, Ernestine and Langedal, Kenneth and Schulz, Christian},
  title =	{{Concurrent Iterated Local Search for the Maximum Weight Independent Set Problem}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{22:1--22:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.22},
  URN =		{urn:nbn:de:0030-drops-232600},
  doi =		{10.4230/LIPIcs.SEA.2025.22},
  annote =	{Keywords: Randomized Local Search, Heuristics, Maximum Weight Independent Set, Algorithm Engineering, Parallel Computing}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.43
On Deleting Vertices to Reduce Density in Graphs and Supermodular Functions

Authors: Karthekeyan Chandrasekaran, Chandra Chekuri, and Shubhang Kulkarni

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

Abstract
We consider deletion problems in graphs and supermodular functions where the goal is to reduce density. In Graph Density Deletion (GraphDD), we are given a graph G = (V,E) with non-negative vertex costs and a non-negative parameter ρ ≥ 0 and the goal is to remove a minimum cost subset S of vertices such that the densest subgraph in G-S has density at most ρ. This problem has an underlying matroidal structure and generalizes several classical problems such as vertex cover, feedback vertex set, and pseudoforest deletion set for appropriately chosen ρ ≤ 1 and all of these classical problems admit a 2-approximation. In sharp contrast, we prove that for every fixed integer ρ > 1, GraphDD is hard to approximate to within a logarithmic factor via a reduction from SetCover, thus showing a phase transition phenomenon. Next, we investigate a generalization of GraphDD to monotone supermodular functions, termed Supermodular Density Deletion (SupmodDD). In SupmodDD, we are given a monotone supermodular function f:2^V → ℤ_{≥0} via an evaluation oracle with element costs and a non-negative integer ρ ≥ 0 and the goal is remove a minimum cost subset S ⊆ V such that the densest subset according to f in V-S has density at most ρ. We show that SupmodDD is approximation equivalent to the well-known Submodular Cover problem; this implies a tight logarithmic approximation and hardness for SupmodDD; it also implies a logarithmic approximation for GraphDD, thus matching our inapproximability bound. Motivated by these hardness results, we design bicriteria approximation algorithms for both GraphDD and SupmodDD.
Cite as

Karthekeyan Chandrasekaran, Chandra Chekuri, and Shubhang Kulkarni. On Deleting Vertices to Reduce Density in Graphs and Supermodular Functions. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 43:1-43:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chandrasekaran_et_al:LIPIcs.ICALP.2025.43,
  author =	{Chandrasekaran, Karthekeyan and Chekuri, Chandra and Kulkarni, Shubhang},
  title =	{{On Deleting Vertices to Reduce Density in Graphs and Supermodular Functions}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{43:1--43:20},
  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.2025.43},
  URN =		{urn:nbn:de:0030-drops-234200},
  doi =		{10.4230/LIPIcs.ICALP.2025.43},
  annote =	{Keywords: Combinatorial Optimization, Approximation Algorithms, Randomized Algorithms, Hardness of Approximation, Densest Subgraph, Supermodular Functions, Submodular Set Cover}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.17
Tight Approximation and Kernelization Bounds for Vertex-Disjoint Shortest Paths

Authors: Matthias Bentert, Fedor V. Fomin, and Petr A. Golovach

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

Abstract
We examine the possibility of approximating Maximum Vertex-Disjoint Shortest Paths. In this problem, the input is an edge-weighted (directed or undirected) n-vertex graph G along with k terminal pairs (s_1,t_1),(s_2,t_2),…,(s_k,t_k). The task is to connect as many terminal pairs as possible by pairwise vertex-disjoint paths such that each path is a shortest path between the respective terminals. Our work is anchored in the recent breakthrough by Lochet [SODA '21], which demonstrates the polynomial-time solvability of the problem for a fixed value of k. Lochet’s result implies the existence of a polynomial-time ck-approximation for Maximum Vertex-Disjoint Shortest Paths, where c ≤ 1 is a constant. (One can guess 1/c terminal pairs to connect in k^O(1/c) time and then utilize Lochet’s algorithm to compute the solution in n^f(1/c) time.) Our first result suggests that this approximation algorithm is, in a sense, the best we can hope for. More precisely, assuming the gap-ETH, we exclude the existence of an o(k)-approximation within f(k) ⋅ poly(n) time for any function f that only depends on k. Our second result demonstrates the infeasibility of achieving an approximation ratio of m^{1/2-ε} in polynomial time, unless P = NP. It is not difficult to show that a greedy algorithm selecting a path with the minimum number of arcs results in a ⌈√𝓁⌉-approximation, where 𝓁 is the number of edges in all the paths of an optimal solution. Since 𝓁 ≤ n, this underscores the tightness of the m^{1/2-ε}-inapproximability bound. Additionally, we establish that Maximum Vertex-Disjoint Shortest Paths is fixed-parameter tractable when parameterized by 𝓁 but does not admit a polynomial kernel. Our hardness results hold for undirected graphs with unit weights, while our positive results extend to scenarios where the input graph is directed and features arbitrary (non-negative) edge weights.
Cite as

Matthias Bentert, Fedor V. Fomin, and Petr A. Golovach. Tight Approximation and Kernelization Bounds for Vertex-Disjoint Shortest Paths. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bentert_et_al:LIPIcs.STACS.2025.17,
  author =	{Bentert, Matthias and Fomin, Fedor V. and Golovach, Petr A.},
  title =	{{Tight Approximation and Kernelization Bounds for Vertex-Disjoint Shortest Paths}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{17:1--17:17},
  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.2025.17},
  URN =		{urn:nbn:de:0030-drops-228422},
  doi =		{10.4230/LIPIcs.STACS.2025.17},
  annote =	{Keywords: Inapproximability, Fixed-parameter tractability, Parameterized approximation}
}
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