30 Search Results for "Koana, Tomohiro"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.36
Kronecker Scaling of Tensors with Applications to Arithmetic Circuits and Algorithms

Authors: Andreas Björklund, Petteri Kaski, Tomohiro Koana, and Jesper Nederlof

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
We show that sufficiently low tensor rank for the balanced tripartitioning tensor P_d(x,y,z) = ∑_{A,B,C ∈ binom([3d],d):A∪ B∪ C = [3d]} x_A y_B z_C for a large enough constant d implies uniform arithmetic circuits for the matrix permanent that are exponentially smaller than circuits obtainable from Ryser’s formula. Under the same low-rank assumption, we obtain exponential-time improvements over the state of the art for a wide variety of related counting and decision problems. Our main methodological contribution is that the tensors P_n have a desirable Kronecker scaling property: They can be decomposed efficiently into a small sum of restrictions of Kronecker powers of P_d for constant d. We prove this with a new technique relying on Steinitz’s lemma, which we hence call Steinitz balancing. As a consequence of our methods, we show that the mentioned low-rank assumption (and hence the improved algorithms) is implied by Strassen’s asymptotic rank conjecture [Progr. Math. 120 (1994)], a bold conjecture that has recently seen intriguing progress.
Cite as

Andreas Björklund, Petteri Kaski, Tomohiro Koana, and Jesper Nederlof. Kronecker Scaling of Tensors with Applications to Arithmetic Circuits and Algorithms. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 36:1-36:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bjorklund_et_al:LIPIcs.ICALP.2026.36,
  author =	{Bj\"{o}rklund, Andreas and Kaski, Petteri and Koana, Tomohiro and Nederlof, Jesper},
  title =	{{Kronecker Scaling of Tensors with Applications to Arithmetic Circuits and Algorithms}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{36:1--36:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.36},
  URN =		{urn:nbn:de:0030-drops-264258},
  doi =		{10.4230/LIPIcs.ICALP.2026.36},
  annote =	{Keywords: tensor rank, Kronecker powers, arithmetic circuits, permanent, parameterized algorithms}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.4
Integer Programming Models for the Median of a 0-1 String Set Under Levenshtein Distance

Authors: Claudio Arbib, Andrea D'Ascenzo, Oya E. Karaşan, and Andrea Pizzuti

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract
The Median String Problem calls for finding a string that minimizes the average distance from a given set of strings. Under the Levenshtein (or edit) metric, the problem is NP-hard even for binary strings. We devised two novel integer linear programming models for this case and tested them against the only formulation we are aware of in the literature. Our numerical experiments attest to the efficacy of the proposed approach.
Cite as

Claudio Arbib, Andrea D'Ascenzo, Oya E. Karaşan, and Andrea Pizzuti. Integer Programming Models for the Median of a 0-1 String Set Under Levenshtein Distance. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{arbib_et_al:LIPIcs.SEA.2026.4,
  author =	{Arbib, Claudio and D'Ascenzo, Andrea and Kara\c{s}an, Oya E. and Pizzuti, Andrea},
  title =	{{Integer Programming Models for the Median of a 0-1 String Set Under Levenshtein Distance}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.4},
  URN =		{urn:nbn:de:0030-drops-260081},
  doi =		{10.4230/LIPIcs.SEA.2026.4},
  annote =	{Keywords: Levenshtein Distance, Median String Problem, Integer Programming}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.39
Faster Approximate Linear Matroid Intersection

Authors: Tatsuya Terao

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
We consider a fast approximation algorithm for the linear matroid intersection problem. In this problem, we are given two r × n matrices M₁ and M₂, and the objective is to find a largest set of columns that are linearly independent in both M₁ and M₂. We design a (1 - ε)-approximation algorithm with time complexity Õ_{ε}(nnz(M₁) + nnz(M₂) + r_{*}^{ω}), where nnz(M_i) denotes the number of nonzero entries in M_i for i = 1, 2, r_{*} denotes the maximum size of a common independent set, and ω < 2.372 denotes the matrix multiplication exponent. Our approximation algorithm is faster than the exact algorithm by Harvey [FOCS'06 & SICOMP'09] and Cheung-Kwok-Lau [STOC'12 & JACM'13], which runs in Õ(nnz(M₁) + nnz(M₂) + n r_{*}^{ω - 1}) time. We also develop a fast (1 - ε)-approximation algorithm for the weighted version of the linear matroid intersection problem. In fact, we design a (1 - ε)-approximation algorithm for weighted linear matroid intersection with time complexity Õ_{ε}(nnz(M₁) + nnz(M₂) + r_{*}^{ω}). Our algorithm improves upon the (1 - ε)-approximation algorithm by Huang-Kakimura-Kamiyama [SODA'16 & Math. Program.'19], which runs in Õ_{ε}(nnz(M₁) + nnz(M₂) + nr_{*}^{ω - 1}) time. To obtain these results, we combine Quanrud’s adaptive sparsification framework [ICALP'24] with a simple yet effective method for efficiently checking whether a given vector lies in the linear span of a subset of vectors, which is of independent interest.
Cite as

Tatsuya Terao. Faster Approximate Linear Matroid Intersection. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 39:1-39:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{terao:LIPIcs.SWAT.2026.39,
  author =	{Terao, Tatsuya},
  title =	{{Faster Approximate Linear Matroid Intersection}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{39:1--39:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.39},
  URN =		{urn:nbn:de:0030-drops-260756},
  doi =		{10.4230/LIPIcs.SWAT.2026.39},
  annote =	{Keywords: Linear matroid intersection, fast approximation algorithm}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.77
Robust Algorithms for Path and Cycle Problems in Geometric Intersection Graphs

Authors: Malory Marin, Jean-Florent Raymond, and Rémi Watrigant

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
We study the design of robust subexponential algorithms for classical connectivity problems on intersection graphs of similarly sized fat objects in ℝ^d. In this setting, each vertex corresponds to a geometric object, and two vertices are adjacent if and only if their objects intersect. We introduce a new tool for designing such algorithms, which we call a λ-linked partition. This is a partition of the vertex set into groups of highly connected vertices. Crucially, such a partition can be computed in polynomial time and does not require access to the geometric representation of the graph. We apply this framework to problems related to paths and cycles in graphs. First, we obtain the first robust ETH-tight algorithms for Hamiltonian Path and Hamiltonian Cycle, running in time 2^O(n^{1-1/d}) on intersection graphs of similarly sized fat objects in ℝ^d. This resolves an open problem of de Berg et al. [STOC 2018] and completes the study of these problems on geometric intersection graphs from the viewpoint of ETH-tight exact algorithms. We further extend our approach to the parameterized setting and design the first robust subexponential parameterized algorithm for Long Path in any fixed dimension d. More precisely, we obtain a randomized robust algorithm running in time 2^O(k^{1-1/d} log² k) n^O(1) on intersection graphs of similarly sized fat objects in ℝ^d, where k is the natural parameter. Besides λ-linked partitions, our algorithm also relies on a low-treewidth pattern covering theorem that we establish for geometric intersection graphs, which may be viewed as a refinement of a result of Marx-Pilipczuk [ESA 2017]. This structural result may be of independent interest.
Cite as

Malory Marin, Jean-Florent Raymond, and Rémi Watrigant. Robust Algorithms for Path and Cycle Problems in Geometric Intersection Graphs. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 77:1-77:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{marin_et_al:LIPIcs.SoCG.2026.77,
  author =	{Marin, Malory and Raymond, Jean-Florent and Watrigant, R\'{e}mi},
  title =	{{Robust Algorithms for Path and Cycle Problems in Geometric Intersection Graphs}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{77:1--77:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.77},
  URN =		{urn:nbn:de:0030-drops-258842},
  doi =		{10.4230/LIPIcs.SoCG.2026.77},
  annote =	{Keywords: Robust algorithms, geometric intersection graphs, subexponential FPT algorithms}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.29
Hitting Geodesic Intervals in Structurally Restricted Graphs

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

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

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

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

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@InProceedings{gima_et_al:LIPIcs.IPEC.2025.29,
  author =	{Gima, Tatsuya and Kobayashi, Yasuaki and Okada, Yuto and Otachi, Yota and Takaike, Hayato},
  title =	{{Hitting Geodesic Intervals in Structurally Restricted Graphs}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.29},
  URN =		{urn:nbn:de:0030-drops-251618},
  doi =		{10.4230/LIPIcs.IPEC.2025.29},
  annote =	{Keywords: Terminal monitoring set, Structural graph parameter, Geodesic interval}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.32
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.
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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.2025.5
Graph Coloring Below Guarantees via Co-Triangle Packing

Authors: Shyan Akmal and Tomohiro Koana

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

Abstract
In the 𝓁-Coloring problem, we are given a graph on n nodes, and tasked with determining if its vertices can be properly colored using 𝓁 colors. In this paper we study below-guarantee graph coloring, which tests whether an n-vertex graph can be properly colored using g-k colors, where g is a trivial upper bound such as n. We introduce an algorithmic framework that builds on a packing of co-triangles K₃ (independent sets of three vertices): the algorithm greedily finds co-triangles and employs a win-win analysis. If many are found, we immediately return yes; otherwise these co-triangles form a small co-triangle modulator, whose deletion makes the graph co-triangle-free. Extending the work of [Gutin et al., SIDMA 2021], who solved 𝓁-Coloring (for any 𝓁) in randomized O^∗(2^k) time when given a K₂-free modulator of size k, we show that this problem can likewise be solved in randomized O^*(2^{k}) time when given a K₃-free modulator of size k. This result in turn yields a randomized O^*(2^{3k/2}) algorithm for (n-k)-Coloring (also known as Dual Coloring), improving the previous O^*(4^k) bound. We then introduce a smaller parameterization, (ω+μ-k)-Coloring, where ω is the clique number and μ is the size of a maximum matching in the complement graph; since ω+μ ≤ n for any graph, this problem is strictly harder. Using the same co-triangle-packing argument, we obtain a randomized O^*(2^{6k}) algorithm, establishing its fixed-parameter tractability for a smaller parameter. Complementing this finding, we show that no fixed-parameter tractable algorithm exists for (ω-k)-Coloring or (μ-k)-Coloring under standard complexity assumptions.
Cite as

Shyan Akmal and Tomohiro Koana. Graph Coloring Below Guarantees via Co-Triangle Packing. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{akmal_et_al:LIPIcs.ISAAC.2025.5,
  author =	{Akmal, Shyan and Koana, Tomohiro},
  title =	{{Graph Coloring Below Guarantees via Co-Triangle Packing}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{5:1--5:16},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-249130},
  doi =		{10.4230/LIPIcs.ISAAC.2025.5},
  annote =	{Keywords: coloring, parameterized algorithms, algebraic algorithms, above-guarantee, below-guarantee, subset convolution, determinants}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.46
Max-Distance Sparsification for Diversification and Clustering

Authors: Soh Kumabe

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

Abstract
Let 𝒟 be a set family that is the solution domain of some combinatorial problem. The max-min diversification problem on 𝒟 is the problem to select k sets from 𝒟 such that the Hamming distance between any two selected sets is at least d. FPT algorithms parameterized by k+𝓁, where 𝓁 = max_{D ∈ 𝒟}|D|, and k+d have been actively studied recently for several specific domains. This paper provides unified algorithmic frameworks to solve this problem. Specifically, for each parameterization k+𝓁 and k+d, we provide an FPT oracle algorithm for the max-min diversification problem using oracles related to 𝒟. We then demonstrate that our frameworks provide the first FPT algorithms on several new domains 𝒟, including the domain of t-linear matroid intersection, almost 2-SAT, minimum edge s,t-flows, vertex sets of s,t-mincut, vertex sets of edge bipartization, and Steiner trees. We also demonstrate that our frameworks generalize most of the existing domain-specific tractability results. Our main technical breakthrough is introducing the notion of max-distance sparsifier of 𝒟, a domain on which the max-min diversification problem is equivalent to the same problem on the original domain 𝒟. The core of our framework is to design FPT oracle algorithms that construct a constant-size max-distance sparsifier of 𝒟. Using max-distance sparsifiers, we provide FPT algorithms for the max-min and max-sum diversification problems on 𝒟, as well as k-center and k-sum-of-radii clustering problems on 𝒟, which are also natural problems in the context of diversification and have their own interests.
Cite as

Soh Kumabe. Max-Distance Sparsification for Diversification and Clustering. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 46:1-46:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kumabe:LIPIcs.ESA.2025.46,
  author =	{Kumabe, Soh},
  title =	{{Max-Distance Sparsification for Diversification and Clustering}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{46:1--46:14},
  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.2025.46},
  URN =		{urn:nbn:de:0030-drops-245146},
  doi =		{10.4230/LIPIcs.ESA.2025.46},
  annote =	{Keywords: Fixed-Parameter Tractability, Diversification, Clustering}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.13
Solving Partial Dominating Set and Related Problems Using Twin-Width

Authors: Jakub Balabán, Daniel Mock, and Peter Rossmanith

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

Abstract
Partial vertex cover and partial dominating set are two well-investigated optimization problems. While they are W[1]-hard on general graphs, they have been shown to be fixed-parameter tractable on many sparse graph classes, including nowhere-dense classes. In this paper, we demonstrate that these problems are also fixed-parameter tractable with respect to the twin-width of a graph. Indeed, we establish a more general result: every graph property that can be expressed by a logical formula of the form ϕ≡∃ x₁⋯ ∃ x_k ∑_{α ∈ I} #y ψ_α(x₁,…,x_k,y) ≥ t, where ψ_α is a quantifier-free formula for each α ∈ I, t is an arbitrary number, and #y is a counting quantifier, can be evaluated in time f(d,k)n, where n is the number of vertices and d is the width of a contraction sequence that is part of the input. In addition to the aforementioned problems, this includes also connected partial dominating set and independent partial dominating set.
Cite as

Jakub Balabán, Daniel Mock, and Peter Rossmanith. Solving Partial Dominating Set and Related Problems Using Twin-Width. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balaban_et_al:LIPIcs.MFCS.2025.13,
  author =	{Balab\'{a}n, Jakub and Mock, Daniel and Rossmanith, Peter},
  title =	{{Solving Partial Dominating Set and Related Problems Using Twin-Width}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.13},
  URN =		{urn:nbn:de:0030-drops-241203},
  doi =		{10.4230/LIPIcs.MFCS.2025.13},
  annote =	{Keywords: Partial Dominating Set, Partial Vertex Cover, meta-algorithm, counting logic, twin-width}
}
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
DOI: 10.4230/LIPIcs.SAND.2025.16
Temporal Dominating Set and Temporal Vertex Cover Under the Lense of Degree Restrictions

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

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

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

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

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@InProceedings{herrmann_et_al:LIPIcs.SAND.2025.16,
  author =	{Herrmann, Anton and Komusiewicz, Christian and Morawietz, Nils and Sommer, Frank},
  title =	{{Temporal Dominating Set and Temporal Vertex Cover Under the Lense of Degree Restrictions}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.16},
  URN =		{urn:nbn:de:0030-drops-230695},
  doi =		{10.4230/LIPIcs.SAND.2025.16},
  annote =	{Keywords: NP-hard problem, FPT-algorithm, Treewidth, Color coding}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.7
Faster Edge Coloring by Partition Sieving

Authors: Shyan Akmal and Tomohiro Koana

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

Abstract
In the Edge Coloring problem, we are given an undirected graph G with n vertices and m edges, and are tasked with finding the smallest positive integer k so that the edges of G can be assigned k colors in such a way that no two edges incident to the same vertex are assigned the same color. Edge Coloring is a classic NP-hard problem, and so significant research has gone into designing fast exponential-time algorithms for solving Edge Coloring and its variants exactly. Prior work showed that Edge Coloring can be solved in 2^mpoly(n) time and polynomial space, and in graphs with average degree d in 2^{(1-ε_d)m}⋅poly(n) time and exponential space, where ε_d = (1/d)^Θ(d³). We present an algorithm that solves Edge Coloring in 2^{m-3n/5}⋅poly(n) time and polynomial space. Our result is the first algorithm for this problem which simultaneously runs in faster than 2^m⋅poly(m) time and uses only polynomial space. In graphs of average degree d, our algorithm runs in 2^{(1-6/(5d))m}⋅poly(n) time, which has far better dependence in d than previous results. We also consider a generalization of Edge Coloring called List Edge Coloring, where each edge e in the input graph comes with a list L_e ⊆ {1, …, k} of colors, and we must determine whether we can assign each edge a color from its list so that no two edges incident to the same vertex receive the same color. We show that this problem can be solved in 2^{(1-6/(5k))m}⋅poly(n) time and polynomial space. The previous best algorithm for List Edge Coloring took 2^m⋅poly(n) time and space. Our algorithms are algebraic, and work by constructing a special polynomial P based off the input graph that contains a multilinear monomial (i.e., a monomial where every variable has degree at most one) if and only if the answer to the List Edge Coloring problem on the input graph is YES. We then solve the problem by detecting multilinear monomials in P. Previous work also employed such monomial detection techniques to solve Edge Coloring. We obtain faster algorithms both by carefully constructing our polynomial P, and by improving the runtimes for certain structured monomial detection problems using a technique we call partition sieving.
Cite as

Shyan Akmal and Tomohiro Koana. Faster Edge Coloring by Partition Sieving. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{akmal_et_al:LIPIcs.STACS.2025.7,
  author =	{Akmal, Shyan and Koana, Tomohiro},
  title =	{{Faster Edge Coloring by Partition Sieving}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{7:1--7:18},
  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.2025.7},
  URN =		{urn:nbn:de:0030-drops-228328},
  doi =		{10.4230/LIPIcs.STACS.2025.7},
  annote =	{Keywords: Coloring, Edge coloring, Chromatic index, Matroid, Pfaffian, Algebraic algorithm}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.62
Faster Algorithms on Linear Delta-Matroids

Authors: Tomohiro Koana and Magnus Wahlström

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

Abstract
We present new algorithms and constructions for linear delta-matroids. Delta-matroids are generalizations of matroids that also capture structures such as matchable vertex sets in graphs and path-packing problems. As with matroids, an important class of delta-matroids is given by linear delta-matroids, which generalize linear matroids and are represented via a "twist" of a skew-symmetric matrix. We observe an alternative representation, termed a contraction representation over a skew-symmetric matrix. This representation is equivalent to the more standard twist representation up to O(n^ω)-time transformations (where n is the dimension of the delta-matroid and ω < 2.372 the matrix multiplication exponent), but it is much more convenient for algorithmic tasks. For instance, the problem of finding a max-weight feasible set now reduces directly to finding a max-weight basis in a linear matroid. Supported by this representation, we provide new algorithms and constructions for linear delta-matroids. In particular, we show that the union and delta-sum of linear delta-matroids are again linear delta-matroids, and that a representation for the resulting delta-matroid can be constructed in randomized time O(n^ω) (or more precisely, in O(n^ω) field operations, over a field of size at least Ω(n⋅(1/ε)), where ε > 0 is an error parameter). Previously, it was only known that these operations define delta-matroids. We also note that every projected linear delta-matroid can be represented as an elementary projection. This implies that several optimization problems over (projected) linear delta-matroids, including the coverage, delta-coverage, and parity problems, reduce (in their decision versions) to a single O(n^ω)-time matrix rank computation. Using the methods of Harvey, previously applied by Cheung, Lao and Leung for linear matroid parity, we furthermore show how to solve the search versions in the same time. This improves on the O(n⁴)-time augmenting path algorithm of Geelen, Iwata and Murota, albeit with randomization. Finally, we consider the maximum-cardinality delta-matroid intersection problem (equivalently, the maximum-cardinality delta-matroid matching problem). Using Storjohann’s algorithms for symbolic determinants, we show that such a solution can be found in O(n^{ω+1}) time. This provides the first (randomized) polynomial-time solution for the problem, thereby solving an open question of Kakimura and Takamatsu.
Cite as

Tomohiro Koana and Magnus Wahlström. Faster Algorithms on Linear Delta-Matroids. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 62:1-62:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koana_et_al:LIPIcs.STACS.2025.62,
  author =	{Koana, Tomohiro and Wahlstr\"{o}m, Magnus},
  title =	{{Faster Algorithms on Linear Delta-Matroids}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{62:1--62:19},
  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.2025.62},
  URN =		{urn:nbn:de:0030-drops-228876},
  doi =		{10.4230/LIPIcs.STACS.2025.62},
  annote =	{Keywords: Delta-matroids, Randomized algorithms}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2024.10
Subexponential Algorithms for Clique Cover on Unit Disk and Unit Ball Graphs

Authors: Tomohiro Koana, Nidhi Purohit, and Kirill Simonov

Published in: LIPIcs, Volume 321, 19th International Symposium on Parameterized and Exact Computation (IPEC 2024)

Abstract
In Clique Cover, given a graph G and an integer k, the task is to partition the vertices of G into k cliques. Clique Cover on unit ball graphs has a natural interpretation as a clustering problem, where the objective function is the maximum diameter of a cluster. Many classical NP-hard problems are known to admit 2^{O(n^{1 - 1/d})}-time algorithms on unit ball graphs in ℝ^d [de Berg et al., SIAM J. Comp 2018]. A notable exception is the Maximum Clique problem, which admits a polynomial-time algorithm on unit disk graphs and a subexponential algorithm on unit ball graphs in ℝ³, but no subexponential algorithm on unit ball graphs in dimensions 4 or larger, assuming the ETH [Bonamy et al., JACM 2021]. In this work, we show that Clique Cover also suffers from a "curse of dimensionality", albeit in a significantly different way compared to Maximum Clique. We present a 2^{O(√n)}-time algorithm for unit disk graphs and argue that it is tight under the ETH. On the other hand, we show that Clique Cover does not admit a 2^{o(n)}-time algorithm on unit ball graphs in dimension 5, unless the ETH fails.
Cite as

Tomohiro Koana, Nidhi Purohit, and Kirill Simonov. Subexponential Algorithms for Clique Cover on Unit Disk and Unit Ball Graphs. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{koana_et_al:LIPIcs.IPEC.2024.10,
  author =	{Koana, Tomohiro and Purohit, Nidhi and Simonov, Kirill},
  title =	{{Subexponential Algorithms for Clique Cover on Unit Disk and Unit Ball Graphs}},
  booktitle =	{19th International Symposium on Parameterized and Exact Computation (IPEC 2024)},
  pages =	{10:1--10:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-353-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{321},
  editor =	{Bonnet, \'{E}douard and Rz\k{a}\.{z}ewski, Pawe{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2024.10},
  URN =		{urn:nbn:de:0030-drops-222369},
  doi =		{10.4230/LIPIcs.IPEC.2024.10},
  annote =	{Keywords: Clique cover, diameter clustering, subexponential algorithms, unit disk graphs}
}
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