18 Search Results for "Tamaki, Hisao"

Document
DOI: 10.4230/LIPIcs.SEA.2026.14
K-Hole Separation in PEO‑Based ILP Treewidth Formulation

Authors: Andrea D'Ascenzo

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

Abstract
In this paper, we introduce a family of valid inequalities for the strongest currently known integer programming formulation of treewidth based on perfect elimination orderings. These inequalities arise from the structure of induced chordless cycles (holes) and strengthen the canonical linear relaxation by enforcing constraints that every feasible chordal completion must satisfy. To handle the exponentially many such inequalities, we develop a dedicated separation routine capable of detecting violated k-hole constraints within a cutting-plane framework. Our computational results show that incorporating these inequalities substantially improves the quality of the lower bounds across a broad range of graph classes, in some cases nearly closing the integrality gap.
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Andrea D'Ascenzo. K-Hole Separation in PEO‑Based ILP Treewidth Formulation. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dascenzo:LIPIcs.SEA.2026.14,
  author =	{D'Ascenzo, Andrea},
  title =	{{K-Hole Separation in PEO‑Based ILP Treewidth Formulation}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{14:1--14:14},
  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.2026.14},
  URN =		{urn:nbn:de:0030-drops-260186},
  doi =		{10.4230/LIPIcs.SEA.2026.14},
  annote =	{Keywords: Treewidth, Integer Linear Programming, Polyhedral Combinatorics, Chordal Completion, Induced Cycles}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.23
Indexing Range Maximum-Sum Segment Queries with Offsets

Authors: Seungbum Jo and Dominik Köppl

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

Abstract
Given an array of n real numbers, the maximum segment sum (MSS) problem is to find a contiguous subarray that has the largest sum. While the MSS problem can be solved optimally with Kadane’s algorithm in O(n) time, the study of its indexing version spawned new extensions such as (a) retrieving the MSS after subtracting a query offset parameter for all array entries or (b) retrieving the MSS for arbitrary query ranges. We here study the combination of both problems (a) and (b), which requires retrieving the MSS for arbitrary query ranges after subtracting a query offset parameter for all array entries. For that, we present an index whose query time is only slower than the best known for (a) by a factor of O(log n). In detail, our index uses O(n log n) space, supports queries in O(log² n) time, and can be constructed in O(n log³ n) time. As side results, we study our combined problem in the context of run-length compressed input, and also deduce a solution for (a) that works in run-length compressed space and time. Finally we give supportive lower bounds for our query problem, showing that there is only a polylogarithmic gap of improvement left.
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Seungbum Jo and Dominik Köppl. Indexing Range Maximum-Sum Segment Queries with Offsets. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 23:1-23:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{jo_et_al:LIPIcs.SWAT.2026.23,
  author =	{Jo, Seungbum and K\"{o}ppl, Dominik},
  title =	{{Indexing Range Maximum-Sum Segment Queries with Offsets}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{23:1--23:16},
  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.2026.23},
  URN =		{urn:nbn:de:0030-drops-260597},
  doi =		{10.4230/LIPIcs.SWAT.2026.23},
  annote =	{Keywords: maximum segment sum, data structure, range query}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2026.98
Interactive Uniform Floodlight Illumination and Rotating Rays Voronoi Diagrams (Media Exposition)

Authors: Carlos Alegría, Ioannis Mantas, Marko Savić, and Martin Suderland

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

Abstract
Floodlight illumination problems are art-gallery variants, where a target domain needs to be illuminated by guards, each associated with a field of view. The rotating rays Voronoi diagram is a Voronoi diagram with rays as sites under the angular distance. There is a natural connection of this Voronoi structure with the problem of finding the minimum aperture such that a given set of uniform aperture floodlights illuminates a target domain. In this work we present an interactive visualization software for such problems, supporting different angular distances, namely, oriented and unoriented versions, and for different domains, namely, the plane and simple polygons.
Cite as

Carlos Alegría, Ioannis Mantas, Marko Savić, and Martin Suderland. Interactive Uniform Floodlight Illumination and Rotating Rays Voronoi Diagrams (Media Exposition). In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 98:1-98:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{alegria_et_al:LIPIcs.SoCG.2026.98,
  author =	{Alegr{\'\i}a, Carlos and Mantas, Ioannis and Savi\'{c}, Marko and Suderland, Martin},
  title =	{{Interactive Uniform Floodlight Illumination and Rotating Rays Voronoi Diagrams}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{98:1--98:7},
  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.2026.98},
  URN =		{urn:nbn:de:0030-drops-259048},
  doi =		{10.4230/LIPIcs.SoCG.2026.98},
  annote =	{Keywords: rotating rays Voronoi diagram, oriented angular distance, unoriented angular distance, Brocard angle, floodlight illumination, coverage problems, visualization software}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.42
Computing Twin-Width via Treedepth and Vertex Integrity

Authors: Robert Ganian and Mathis Rocton

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

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

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

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@InProceedings{ganian_et_al:LIPIcs.STACS.2026.42,
  author =	{Ganian, Robert and Rocton, Mathis},
  title =	{{Computing Twin-Width via Treedepth and Vertex Integrity}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{42:1--42:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.42},
  URN =		{urn:nbn:de:0030-drops-255318},
  doi =		{10.4230/LIPIcs.STACS.2026.42},
  annote =	{Keywords: twin-width, fixed-parameter algorithms, treedepth, vertex integrity}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.21
A Polynomial Delay Algorithm Generating All Potential Maximal Cliques in Triconnected Planar Graphs

Authors: Alexander Grigoriev, Yasuaki Kobayashi, Hisao Tamaki, and Tom C. van der Zanden

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

Abstract
We develop a new characterization of potential maximal cliques of a triconnected planar graph and, using this characterization, give a polynomial delay algorithm generating all potential maximal cliques of a given triconnected planar graph. Combined with the dynamic programming algorithm due to Bouchitté and Todinca, this algorithm leads to a treewidth algorithm for general planar graphs that runs in time linear in the number of potential maximal cliques and polynomial in the number of vertices.
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Alexander Grigoriev, Yasuaki Kobayashi, Hisao Tamaki, and Tom C. van der Zanden. A Polynomial Delay Algorithm Generating All Potential Maximal Cliques in Triconnected Planar Graphs. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{grigoriev_et_al:LIPIcs.IPEC.2025.21,
  author =	{Grigoriev, Alexander and Kobayashi, Yasuaki and Tamaki, Hisao and van der Zanden, Tom C.},
  title =	{{A Polynomial Delay Algorithm Generating All Potential Maximal Cliques in Triconnected Planar Graphs}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{21:1--21:17},
  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.2025.21},
  URN =		{urn:nbn:de:0030-drops-251530},
  doi =		{10.4230/LIPIcs.IPEC.2025.21},
  annote =	{Keywords: potential maximal cliques, treewidth, planar graphs, triconnected planar graphs, polynomial delay generation}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.20
Routing Few Robots in a Crowded Network

Authors: Argyrios Deligkas, Eduard Eiben, Robert Ganian, Iyad Kanj, Dominik Leko, and M. S. Ramanujan

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

Abstract
In Graph Coordinated Motion Planning, we are given a graph G some of whose vertices are occupied by robots, and we are asked to route k marked robots to their destinations while avoiding collisions and without exceeding a given budget 𝓁 on the number of robot moves. We continue the recent investigation of the problem [ICALP 2024], focusing on the parameter k that captures the task of routing a small number of robots in a possibly crowded graph. We prove that the problem is W[1]-hard parameterized by 𝓁 even for k = 1, but fixed-parameter tractable parameterized by k plus the treedepth of G. We complement the latter algorithm with an NP-hardness reduction which shows that both parameters are necessary to achieve tractability.
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Argyrios Deligkas, Eduard Eiben, Robert Ganian, Iyad Kanj, Dominik Leko, and M. S. Ramanujan. Routing Few Robots in a Crowded Network. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{deligkas_et_al:LIPIcs.WADS.2025.20,
  author =	{Deligkas, Argyrios and Eiben, Eduard and Ganian, Robert and Kanj, Iyad and Leko, Dominik and Ramanujan, M. S.},
  title =	{{Routing Few Robots in a Crowded Network}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{20:1--20:15},
  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.2025.20},
  URN =		{urn:nbn:de:0030-drops-242516},
  doi =		{10.4230/LIPIcs.WADS.2025.20},
  annote =	{Keywords: graph coordinated motion planning, parameterized complexity, treedepth}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.93
Improved Approximation Algorithms for Capacitated Vehicle Routing with Fixed Capacity

Authors: Jingyang Zhao and Mingyu Xiao

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

Abstract
The Capacitated Vehicle Routing Problem (CVRP) is one of the most extensively studied problems in combinatorial optimization. Based on customer demand, we distinguish three variants of CVRP: unit-demand, splittable, and unsplittable. In this paper, we consider k-CVRP in general metrics and on general graphs, where k is the vehicle capacity. All three versions are APX-hard for any fixed k ≥ 3. Assume that the approximation ratio of metric TSP is 3/2. We present a (5/2 - Θ(√{1/k}))-approximation algorithm for the splittable and unit-demand cases, and a (5/2 + ln 2 - Θ(√{1/k}))-approximation algorithm for the unsplittable case. Our approximation ratio is better than the previous results when k is less than a sufficiently large value, approximately 1.7 x 10⁷. For small values of k, we design independent and elegant algorithms with further improvements. For the splittable and unit-demand cases, we improve the approximation ratio from 1.792 to 1.500 for k = 3, and from 1.750 to 1.500 for k = 4. For the unsplittable case, we improve the approximation ratio from 1.792 to 1.500 for k = 3, from 2.051 to 1.750 for k = 4, and from 2.249 to 2.157 for k = 5. The approximation ratio for k = 3 surprisingly achieves the same value as in the splittable case. Our techniques, such as EX-ITP - an extension of the classic ITP method, have the potential to improve algorithms for other routing problems as well.
Cite as

Jingyang Zhao and Mingyu Xiao. Improved Approximation Algorithms for Capacitated Vehicle Routing with Fixed Capacity. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 93:1-93:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zhao_et_al:LIPIcs.MFCS.2025.93,
  author =	{Zhao, Jingyang and Xiao, Mingyu},
  title =	{{Improved Approximation Algorithms for Capacitated Vehicle Routing with Fixed Capacity}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{93:1--93:19},
  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.2025.93},
  URN =		{urn:nbn:de:0030-drops-242008},
  doi =		{10.4230/LIPIcs.MFCS.2025.93},
  annote =	{Keywords: Combinatorial Optimization, Capacitated Vehicle Routing, Approximation Algorithms, Graph Algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.131
Deterministic Complexity Analysis of Hermitian Eigenproblems

Authors: Aleksandros Sobczyk

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

Abstract
In this work we revisit the arithmetic and bit complexity of Hermitian eigenproblems. Recently, [BGVKS, FOCS 2020] proved that a (non-Hermitian) matrix A can be diagonalized with a randomized algorithm in O(n^{ω}log²(n/ε)) arithmetic operations, where ω≲ 2.371 is the square matrix multiplication exponent, and [Shah, SODA 2025] significantly improved the bit complexity for the Hermitian case. Our main goal is to obtain similar deterministic complexity bounds for various Hermitian eigenproblems. In the Real RAM model, we show that a Hermitian matrix can be diagonalized deterministically in O(n^{ω}log(n)+n²polylog(n/ε)) arithmetic operations, improving the classic deterministic Õ(n³) algorithms, and derandomizing the aforementioned state-of-the-art. The main technical step is a complete, detailed analysis of a well-known divide-and-conquer tridiagonal eigensolver of Gu and Eisenstat [GE95], when accelerated with the Fast Multipole Method, asserting that it can accurately diagonalize a symmetric tridiagonal matrix in nearly-O(n²) operations. In finite precision, we show that an algorithm by Schönhage [Sch72] to reduce a Hermitian matrix to tridiagonal form is stable in the floating point model, using O(log(n/ε)) bits of precision. This leads to a deterministic algorithm to compute all the eigenvalues of a Hermitian matrix in O(n^{ω}ℱ(log(n/ε)) + n²polylog(n/ε)) bit operations, where ℱ(b) ∈ Õ(b) is the bit complexity of a single floating point operation on b bits. This improves the best known Õ(n³) deterministic and O(n^{ω}log²(n/ε)ℱ(log(n/ε))) randomized complexities. We conclude with some other useful subroutines such as computing spectral gaps, condition numbers, and spectral projectors, and with some open problems.
Cite as

Aleksandros Sobczyk. Deterministic Complexity Analysis of Hermitian Eigenproblems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 131:1-131:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sobczyk:LIPIcs.ICALP.2025.131,
  author =	{Sobczyk, Aleksandros},
  title =	{{Deterministic Complexity Analysis of Hermitian Eigenproblems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{131:1--131:21},
  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.2025.131},
  URN =		{urn:nbn:de:0030-drops-235081},
  doi =		{10.4230/LIPIcs.ICALP.2025.131},
  annote =	{Keywords: Hermitian eigenproblem, eigenvalues, SVD, tridiagonal reduction, matrix multiplication time, diagonalization, bit complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.90
Revisiting Directed Disjoint Paths on Tournaments (And Relatives)

Authors: Guilherme de C. M. Gomes, Raul Lopes, and Ignasi Sau

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

Abstract
In the Directed Disjoint Paths problem (k-DDP), we are given a digraph and k pairs of terminals, and the goal is to find k pairwise vertex-disjoint paths connecting each pair of terminals. Bang-Jensen and Thomassen [SIAM J. Discrete Math. 1992] claimed that k-DDP is NP-complete on tournaments, and this result triggered a very active line of research about the complexity of the problem on tournaments and natural superclasses. We identify a flaw in their proof, which has been acknowledged by the authors, and provide a new NP-completeness proof. From an algorithmic point of view, Fomin and Pilipczuk [J. Comb. Theory B 2019] provided an FPT algorithm for the edge-disjoint version of the problem on semicomplete digraphs, and showed that their technique cannot work for the vertex-disjoint version. We overcome this obstacle by showing that the version of k-DDP where we allow congestion c on the vertices is FPT on semicomplete digraphs provided that c is greater than k/2. This is based on a quite elaborate irrelevant vertex argument inspired by the edge-disjoint version, and we show that our choice of c is best possible for this technique, with a counterexample with no irrelevant vertices when c ≤ k/2. We also prove that k-DDP on digraphs that can be partitioned into h semicomplete digraphs is W[1]-hard parameterized by k+h, which shows that the XP algorithm presented by Chudnovsky, Scott, and Seymour [J. Comb. Theory B 2019] is essentially optimal.
Cite as

Guilherme de C. M. Gomes, Raul Lopes, and Ignasi Sau. Revisiting Directed Disjoint Paths on Tournaments (And Relatives). In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 90:1-90:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dec.m.gomes_et_al:LIPIcs.ICALP.2025.90,
  author =	{de C. M. Gomes, Guilherme and Lopes, Raul and Sau, Ignasi},
  title =	{{Revisiting Directed Disjoint Paths on Tournaments (And Relatives)}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{90:1--90:20},
  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.2025.90},
  URN =		{urn:nbn:de:0030-drops-234678},
  doi =		{10.4230/LIPIcs.ICALP.2025.90},
  annote =	{Keywords: directed graphs, tournaments, semicomplete digraphs, directed disjoint paths, congestion, parameterized complexity, directed pathwidth}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.44
A Minor-Testing Approach for Coordinated Motion Planning with Sliding Robots

Authors: Eduard Eiben, Robert Ganian, Iyad Kanj, and M. S. Ramanujan

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We study a variant of the Coordinated Motion Planning problem on undirected graphs, referred to herein as the Coordinated Sliding-Motion Planning (CSMP) problem. In this variant, we are given an undirected graph G, k robots R₁,… ,R_k positioned on distinct vertices of G, p ≤ k distinct destination vertices for robots R₁,… ,R_p, and 𝓁 ∈ ℕ. The problem is to decide if there is a serial schedule of at most 𝓁 moves (i.e., of makespan 𝓁) such that at the end of the schedule each robot with a destination reaches it, where a robot’s move is a free path (unoccupied by any robots) from its current position to an unoccupied vertex. The problem is known to be NP-hard even on full grids. It has been studied in several contexts, including coin movement and reconfiguration problems, with respect to feasibility, complexity, and approximation. Geometric variants of the problem, in which congruent geometric-shape robots (e.g., unit disk/squares) slide or translate in the Euclidean plane, have also been studied extensively. We investigate the parameterized complexity of CSMP with respect to two parameters: the number k of robots and the makespan 𝓁. As our first result, we present a fixed-parameter algorithm for CSMP parameterized by k. For our second result, we present a fixed-parameter algorithm parameterized by 𝓁 for the special case of CSMP in which only a single robot has a destination and the graph is planar. A crucial new ingredient for both of our results is that the solution admits a succinct representation as a small labeled topological minor of the input graph.
Cite as

Eduard Eiben, Robert Ganian, Iyad Kanj, and M. S. Ramanujan. A Minor-Testing Approach for Coordinated Motion Planning with Sliding Robots. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 44:1-44:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{eiben_et_al:LIPIcs.SoCG.2025.44,
  author =	{Eiben, Eduard and Ganian, Robert and Kanj, Iyad and Ramanujan, M. S.},
  title =	{{A Minor-Testing Approach for Coordinated Motion Planning with Sliding Robots}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{44:1--44:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.44},
  URN =		{urn:nbn:de:0030-drops-231966},
  doi =		{10.4230/LIPIcs.SoCG.2025.44},
  annote =	{Keywords: coordinated motion planning on graphs, parameterized complexity, topological minor testing, planar graphs}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.65
Recognizing 2-Layer and Outer k-Planar Graphs

Authors: Yasuaki Kobayashi, Yuto Okada, and Alexander Wolff

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
The crossing number of a graph is the least number of crossings over all drawings of the graph in the plane. Computing the crossing number of a given graph is NP-hard, but fixed-parameter tractable (FPT) with respect to the natural parameter. Two well-known variants of the problem are 2-layer crossing minimization and circular crossing minimization, where every vertex must lie on one of two layers, namely two parallel lines, or a circle, respectively. In both cases, edges are drawn as straight-line segments. Both variants are NP-hard, but admit FPT-algorithms with respect to the natural parameter. In recent years, in the context of beyond-planar graphs, a local version of the crossing number has also received considerable attention. A graph is k-planar if it admits a drawing with at most k crossings per edge. In contrast to the crossing number, recognizing k-planar graphs is NP-hard even if k = 1 and hence not likely to be FPT with respect to the natural parameter k. In this paper, we consider the two above variants in the local setting. The k-planar graphs that admit a straight-line drawing with vertices on two layers or on a circle are called 2-layer k-planar and outer k-planar graphs, respectively. We study the parameterized complexity of the two recognition problems with respect to the natural parameter k. For k = 0, the two classes of graphs are exactly the caterpillars and outerplanar graphs, respectively, which can be recognized in linear time. Two groups of researchers independently showed that outer 1-planar graphs can also be recognized in linear time [Hong et al., Algorithmica 2015; Auer et al., Algorithmica 2016]. One group asked explicitly whether outer 2-planar graphs can be recognized in polynomial time. Our main contribution consists of XP-algorithms for recognizing 2-layer k-planar graphs and outer k-planar graphs, which implies that both recognition problems can be solved in polynomial time for every fixed k. We complement these results by showing that recognizing 2-layer k-planar graphs is XNLP-complete and that recognizing outer k-planar graphs is XNLP-hard. This implies that both problems are W[t]-hard for every t and that it is unlikely that they admit FPT-algorithms. On the other hand, we present an FPT-algorithm for recognizing 2-layer k-planar graphs where the order of the vertices on one layer is specified.
Cite as

Yasuaki Kobayashi, Yuto Okada, and Alexander Wolff. Recognizing 2-Layer and Outer k-Planar Graphs. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 65:1-65:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kobayashi_et_al:LIPIcs.SoCG.2025.65,
  author =	{Kobayashi, Yasuaki and Okada, Yuto and Wolff, Alexander},
  title =	{{Recognizing 2-Layer and Outer k-Planar Graphs}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{65:1--65:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.65},
  URN =		{urn:nbn:de:0030-drops-232170},
  doi =		{10.4230/LIPIcs.SoCG.2025.65},
  annote =	{Keywords: 2-layer k-planar graphs, outer k-planar graphs, recognition algorithms, local crossing number, bandwidth, FPT, XNLP, XP, W\lbrackt\rbrack}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.12
Restless Exploration and Token Dissemination in Vertex-Permuted Temporal Graphs

Authors: Kamran Ayoubi and Lata Narayanan

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

Abstract
In the temporal graph exploration problem, an agent wishes to visit all the vertices of a temporal graph, moving at most one edge in every time step. In restless exploration, the agent is required to move in every step, and cannot wait at a vertex. We study the problem of restless exploration in vertex-permuted graphs, which are a class of temporal graphs in which the topology of the graph stays the same in every time step. In other words, in a vertex permuted temporal graph, in every step i, the graph G_i is isomorphic to the same base graph G. We give a precise characterization of graphs G such that restless exploration is possible in every vertex-permuted graph with base graph G. Our technique is based on an a characterization of networks in which there is an online distributed algorithm for restless token dissemination. Finally we describe some families of graphs in which restless exploration is always possible, and some in which it is not.
Cite as

Kamran Ayoubi and Lata Narayanan. Restless Exploration and Token Dissemination in Vertex-Permuted Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ayoubi_et_al:LIPIcs.SAND.2025.12,
  author =	{Ayoubi, Kamran and Narayanan, Lata},
  title =	{{Restless Exploration and Token Dissemination in Vertex-Permuted Temporal Graphs}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{12:1--12:17},
  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.2025.12},
  URN =		{urn:nbn:de:0030-drops-230658},
  doi =		{10.4230/LIPIcs.SAND.2025.12},
  annote =	{Keywords: Temporal graphs, Vertex permuted graphs, Restless exploration, Periodic graphs, Token dissemination}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.15
Exponential-Time Approximation (Schemes) for Vertex-Ordering Problems

Authors: Matthias Bentert, Fedor V. Fomin, Tanmay Inamdar, and Saket Saurabh

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

Abstract
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest known (exponential-time) exact algorithms and the best known approximation factors that can be achieved in polynomial time? Following the recent research initiated by Esmer et al. (ESA 2022, IPEC 2023, SODA 2024) on vertex-subset problems, and by Inamdar et al. (ITCS 2024) on graph-partitioning problems, we focus on vertex-ordering problems. In particular, we give positive results for Feedback Arc Set, Optimal Linear Arrangement, Cutwidth, and Pathwidth. Most of our algorithms build upon a novel "balanced-cut" approach - which is our main conceptual contribution. This allows us to solve various problems in very general settings allowing for directed and arc-weighted input graphs. Our main technical contribution is a (1+ε)-approximation for any ε > 0 for (weighted) Feedback Arc Set in O^*((2-δ_ε)^n) time, where δ_ε > 0 is a constant only depending on ε.
Cite as

Matthias Bentert, Fedor V. Fomin, Tanmay Inamdar, and Saket Saurabh. Exponential-Time Approximation (Schemes) for Vertex-Ordering Problems. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bentert_et_al:LIPIcs.ITCS.2025.15,
  author =	{Bentert, Matthias and Fomin, Fedor V. and Inamdar, Tanmay and Saurabh, Saket},
  title =	{{Exponential-Time Approximation (Schemes) for Vertex-Ordering Problems}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.15},
  URN =		{urn:nbn:de:0030-drops-226431},
  doi =		{10.4230/LIPIcs.ITCS.2025.15},
  annote =	{Keywords: Feedback Arc Set, Cutwidth, Optimal Linear Arrangement, Pathwidth}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2023.34
A Contraction-Recursive Algorithm for Treewidth

Authors: Hisao Tamaki

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract
Let tw(G) denote the treewidth of graph G. Given a graph G and a positive integer k such that tw(G) ≤ k + 1, we are to decide if tw(G) ≤ k. We give a certifying algorithm RTW ("R" for recursive) for this task: it returns one or more tree-decompositions of G of width ≤ k if the answer is YES and a minimal contraction H of G such that tw(H) > k otherwise. Starting from a greedy upper bound on tw(G) and repeatedly improving the upper bound by this algorithm, we obtain tw(G) with certificates. RTW uses a heuristic variant of Tamaki’s PID algorithm for treewidth (ESA2017), which we call HPID. Informally speaking, PID builds potential subtrees of tree-decompositions of width ≤ k in a bottom up manner, until such a tree-decomposition is constructed or the set of potential subtrees is exhausted without success. HPID uses the same method of generating a new subtree from existing ones but with a different generation order which is not intended for exhaustion but for quick generation of a full tree-decomposition when possible. RTW, given G and k, interleaves the execution of HPID with recursive calls on G /e for edges e of G, where G / e denotes the graph obtained from G by contracting edge e. If we find that tw(G / e) > k, then we have tw(G) > k with the same certificate. If we find that tw(G / e) ≤ k, we "uncontract" the bags of the certifying tree-decompositions of G / e into bags of G and feed them to HPID to help progress. If the question is not resolved after the recursive calls are made for all edges, we finish HPID in an exhaustive mode. If it turns out that tw(G) > k, then G is a certificate for tw(G') > k for every G' of which G is a contraction, because we have found tw(G / e) ≤ k for every edge e of G. This final round of HPID guarantees the correctness of the algorithm, while its practical efficiency derives from our methods of "uncontracting" bags of tree-decompositions of G / e to useful bags of G, as well as of exploiting those bags in HPID. Experiments show that our algorithm drastically extends the scope of practically solvable instances. In particular, when applied to the 100 instances in the PACE 2017 bonus set, the number of instances solved by our implementation on a typical laptop, with the timeout of 100, 1000, and 10000 seconds per instance, are 72, 92, and 98 respectively, while these numbers are 11, 38, and 68 for Tamaki’s PID solver and 65, 82, and 85 for his new solver (SEA 2022).
Cite as

Hisao Tamaki. A Contraction-Recursive Algorithm for Treewidth. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{tamaki:LIPIcs.IPEC.2023.34,
  author =	{Tamaki, Hisao},
  title =	{{A Contraction-Recursive Algorithm for Treewidth}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.34},
  URN =		{urn:nbn:de:0030-drops-194536},
  doi =		{10.4230/LIPIcs.IPEC.2023.34},
  annote =	{Keywords: graph algorithm, treewidth, exact computation, BT dynamic programming, contraction, certifying algorithms}
}
Document
DOI: 10.4230/LIPIcs.SEA.2022.17
Heuristic Computation of Exact Treewidth

Authors: Hisao Tamaki

Published in: LIPIcs, Volume 233, 20th International Symposium on Experimental Algorithms (SEA 2022)

Abstract
We are interested in computing the treewidth tw(G) of a given graph G. Our approach is to design heuristic algorithms for computing a sequence of improving upper bounds and a sequence of improving lower bounds, which would hopefully converge to tw(G) from both sides. The upper bound algorithm extends and simplifies the present author’s unpublished work on a heuristic use of the dynamic programming algorithm for deciding treewidth due to Bouchitté and Todinca. The lower bound algorithm is based on the well-known fact that, for every minor H of G, we have tw(H) ≤ tw(G). Starting from a greedily computed minor H_0 of G, the algorithm tries to construct a sequence of minors H_0, H_1, ..., H_k with tw(H_i) < tw(H_{i + 1}) for 0 ≤ i < k and hopefully tw(H_k) = tw(G). We have implemented a treewidth solver based on this approach and have evaluated it on the bonus instances from the exact treewidth track of PACE 2017 algorithm implementation challenge. The results show that our approach is extremely effective in tackling instances that are hard for conventional solvers. Our solver has an additional advantage over conventional ones in that it attaches a compact certificate to the lower bound it computes.
Cite as

Hisao Tamaki. Heuristic Computation of Exact Treewidth. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{tamaki:LIPIcs.SEA.2022.17,
  author =	{Tamaki, Hisao},
  title =	{{Heuristic Computation of Exact Treewidth}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2022.17},
  URN =		{urn:nbn:de:0030-drops-165512},
  doi =		{10.4230/LIPIcs.SEA.2022.17},
  annote =	{Keywords: graph algorithm, treewidth, heuristics, BT dynamic programming, contraction, obstruction, minimal forbidden minor, certifying algorithms}
}
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