8 Search Results for "Kumabe, Soh"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.53
Average Sensitivity of Geometric Algorithms

Authors: Matthijs Ebbens and Yuichi Yoshida

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

Abstract
In modern applications of geometric algorithms, it is often unrealistic to assume that the input representation fully captures all relevant aspects of the problem, because the input data is often large and dynamic. To address this challenge, we consider the notion of average sensitivity, which is defined as the average earth mover’s distance between the output distributions of the algorithm when run on an input and the same input with one point removed, where the average is over removed points and the distance between two outputs is measured using the symmetric difference size. We start by showing that a number of classical problems from computational geometry, in particular the convex hull, Delaunay triangulation, and Voronoi diagram problems, are "simple" from the viewpoint of average sensitivity by proving tight bounds for the average sensitivity of any algorithm for these problems. Then, we continue by constructing an algorithm with low average sensitivity that computes, for any ε > 0, a set of (1/3+ε)n guards for the art gallery problem. This is the main technical contribution of this work, which combines algorithms from computational geometry with results from the theory of local computation algorithms (LCAs) and property testing.
Cite as

Matthijs Ebbens and Yuichi Yoshida. Average Sensitivity of Geometric Algorithms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 53:1-53:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ebbens_et_al:LIPIcs.ITCS.2026.53,
  author =	{Ebbens, Matthijs and Yoshida, Yuichi},
  title =	{{Average Sensitivity of Geometric Algorithms}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{53:1--53:16},
  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.2026.53},
  URN =		{urn:nbn:de:0030-drops-253409},
  doi =		{10.4230/LIPIcs.ITCS.2026.53},
  annote =	{Keywords: Average Sensitivity, Convex Hull, Delaunay Triangulation, Voronoi Diagram, Art Gallery}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.48
Quadratic Kernel for Cliques or Trees Vertex Deletion

Authors: Soh Kumabe

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

Abstract
We consider Cliques or Trees Vertex Deletion, which is a hybrid of two fundamental parameterized problems: Cluster Vertex Deletion and Feedback Vertex Set. In this problem, we are given an undirected graph G and an integer k, and asked to find a vertex subset X of size at most k such that each connected component of G-X is either a clique or a tree. Jacob et al. (ISAAC, 2024) provided a kernel of O(k⁵) vertices for this problem, which was recently improved to O(k⁴) by Tsur (IPL, 2025). Our main result is a kernel of O(k²) vertices. This result closes the gap between the kernelization result for Feedback Vertex Set, which corresponds to the case where each connected component of G-X must be a tree. Although both cluster vertex deletion number and feedback vertex set number are well-studied structural parameters, little attention has been given to parameters that generalize both of them. In fact, the lowest common well-known generalization of them is clique-width, which is a highly general parameter. To fill the gap here, we initiate the study of the cliques or trees vertex deletion number as a structural parameter. We prove that Longest Cycle, which is a fundamental problem that does not admit o(n^k)-time algorithm unless ETH fails when k is the clique-width, becomes fixed-parameter tractable when parameterized by the cliques or trees vertex deletion number.
Cite as

Soh Kumabe. Quadratic Kernel for Cliques or Trees Vertex Deletion. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 48:1-48:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kumabe:LIPIcs.ISAAC.2025.48,
  author =	{Kumabe, Soh},
  title =	{{Quadratic Kernel for Cliques or Trees Vertex Deletion}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{48:1--48:15},
  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.2025.48},
  URN =		{urn:nbn:de:0030-drops-249568},
  doi =		{10.4230/LIPIcs.ISAAC.2025.48},
  annote =	{Keywords: Fixed-Parameter Tractability, Kernelization, Deletion to Scattered Graph Classes, Cluster Vertex Deletion, Feedback Vertex Set}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.11
Finding Diverse Solutions in Combinatorial Problems with a Distributive Lattice Structure

Authors: Mark de Berg, Andrés López Martínez, and Frits Spieksma

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

Abstract
We generalize the polynomial-time solvability of k-Diverse Minimum s-t Cuts (De Berg et al., ISAAC'23) to a wider class of combinatorial problems whose solution sets have a distributive lattice structure. We identify three structural conditions that, when met by a problem, ensure that a k-sized multiset of maximally-diverse solutions - measured by the sum of pairwise Hamming distances - can be found in polynomial time. We apply this framework to obtain polynomial-time algorithms for finding diverse minimum s-t cuts, diverse stable matchings, and diverse market-clearing price vectors. Moreover, we show that the framework extends to two other natural measures of diversity. Lastly, we present a simpler algorithmic framework for finding a largest set of pairwise disjoint solutions in problems that meet these structural conditions.
Cite as

Mark de Berg, Andrés López Martínez, and Frits Spieksma. Finding Diverse Solutions in Combinatorial Problems with a Distributive Lattice Structure. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{deberg_et_al:LIPIcs.ISAAC.2025.11,
  author =	{de Berg, Mark and L\'{o}pez Mart{\'\i}nez, Andr\'{e}s and Spieksma, Frits},
  title =	{{Finding Diverse Solutions in Combinatorial Problems with a Distributive Lattice Structure}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{11:1--11:19},
  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.2025.11},
  URN =		{urn:nbn:de:0030-drops-249197},
  doi =		{10.4230/LIPIcs.ISAAC.2025.11},
  annote =	{Keywords: Diversity, Lattice Theory, Submodular Function Minimization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.11
Courcelle’s Theorem for Lipschitz Continuity

Authors: Tatsuya Gima, Soh Kumabe, and Yuichi Yoshida

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

Abstract
Lipschitz continuity of algorithms, introduced by Kumabe and Yoshida (FOCS'23), measures the stability of an algorithm against small input perturbations. Algorithms with small Lipschitz continuity are desirable, as they ensure reliable decision-making and reproducible scientific research. Several studies have proposed Lipschitz continuous algorithms for various combinatorial optimization problems, but these algorithms are problem-specific, requiring a separate design for each problem. To address this issue, we provide the first algorithmic meta-theorem in the field of Lipschitz continuous algorithms. Our result can be seen as a Lipschitz continuous analogue of Courcelle’s theorem, which offers Lipschitz continuous algorithms for problems on bounded-treewidth graphs. Specifically, we consider the problem of finding a vertex set in a graph that maximizes or minimizes the total weight, subject to constraints expressed in monadic second-order logic (MSO₂). We show that for any ε > 0, there exists a (1±ε)-approximation algorithm for the problem with a polylogarithmic Lipschitz constant on bounded treewidth graphs. On such graphs, our result outperforms most existing Lipschitz continuous algorithms in terms of approximability and/or Lipschitz continuity. Further, we provide similar results for problems on bounded-clique-width graphs subject to constraints expressed in MSO₁. Additionally, we construct a Lipschitz continuous version of Baker’s decomposition using our meta-theorem as a subroutine.
Cite as

Tatsuya Gima, Soh Kumabe, and Yuichi Yoshida. Courcelle’s Theorem for Lipschitz Continuity. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gima_et_al:LIPIcs.ESA.2025.11,
  author =	{Gima, Tatsuya and Kumabe, Soh and Yoshida, Yuichi},
  title =	{{Courcelle’s Theorem for Lipschitz Continuity}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{11:1--11:14},
  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.2025.11},
  URN =		{urn:nbn:de:0030-drops-244793},
  doi =		{10.4230/LIPIcs.ESA.2025.11},
  annote =	{Keywords: Fixed-Parameter Tractability, Algorithmic Meta-Theorem, Lipschitz Continuity}
}
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
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.102
Lipschitz Continuous Allocations for Optimization Games

Authors: Soh Kumabe and Yuichi Yoshida

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
In cooperative game theory, the primary focus is the equitable allocation of payoffs or costs among agents. However, in the practical applications of cooperative games, accurately representing games is challenging. In such cases, using an allocation method sensitive to small perturbations in the game can lead to various problems, including dissatisfaction among agents and the potential for manipulation by agents seeking to maximize their own benefits. Therefore, the allocation method must be robust against game perturbations. In this study, we explore optimization games, in which the value of the characteristic function is provided as the optimal value of an optimization problem. To assess the robustness of the allocation methods, we use the Lipschitz constant, which quantifies the extent of change in the allocation vector in response to a unit perturbation in the weight vector of the underlying problem. Thereafter, we provide an algorithm for the matching game that returns an allocation belonging to the (1/2-ε)-approximate core with Lipschitz constant O(ε^{-1}). Additionally, we provide an algorithm for a minimum spanning tree game that returns an allocation belonging to the 4-approximate core with a constant Lipschitz constant. The Shapley value is a popular allocation that satisfies several desirable properties. Therefore, we investigate the robustness of the Shapley value. We demonstrate that the Lipschitz constant of the Shapley value for the minimum spanning tree is constant, whereas that for the matching game is Ω(log n), where n denotes the number of vertices.
Cite as

Soh Kumabe and Yuichi Yoshida. Lipschitz Continuous Allocations for Optimization Games. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 102:1-102:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kumabe_et_al:LIPIcs.ICALP.2024.102,
  author =	{Kumabe, Soh and Yoshida, Yuichi},
  title =	{{Lipschitz Continuous Allocations for Optimization Games}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{102:1--102:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.102},
  URN =		{urn:nbn:de:0030-drops-202456},
  doi =		{10.4230/LIPIcs.ICALP.2024.102},
  annote =	{Keywords: Cooperative Games, Lipschitz Continuity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.75
Average Sensitivity of the Knapsack Problem

Authors: Soh Kumabe and Yuichi Yoshida

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
In resource allocation, we often require that the output allocation of an algorithm is stable against input perturbation because frequent reallocation is costly and untrustworthy. Varma and Yoshida (SODA'21) formalized this requirement for algorithms as the notion of average sensitivity. Here, the average sensitivity of an algorithm on an input instance is, roughly speaking, the average size of the symmetric difference of the output for the instance and that for the instance with one item deleted, where the average is taken over the deleted item. In this work, we consider the average sensitivity of the knapsack problem, a representative example of a resource allocation problem. We first show a (1-ε)-approximation algorithm for the knapsack problem with average sensitivity O(ε^{-1}log ε^{-1}). Then, we complement this result by showing that any (1-ε)-approximation algorithm has average sensitivity Ω(ε^{-1}). As an application of our algorithm, we consider the incremental knapsack problem in the random-order setting, where the goal is to maintain a good solution while items arrive one by one in a random order. Specifically, we show that for any ε > 0, there exists a (1-ε)-approximation algorithm with amortized recourse O(ε^{-1}log ε^{-1}) and amortized update time O(log n+f_ε), where n is the total number of items and f_ε > 0 is a value depending on ε.
Cite as

Soh Kumabe and Yuichi Yoshida. Average Sensitivity of the Knapsack Problem. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 75:1-75:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kumabe_et_al:LIPIcs.ESA.2022.75,
  author =	{Kumabe, Soh and Yoshida, Yuichi},
  title =	{{Average Sensitivity of the Knapsack Problem}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{75:1--75:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva 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.2022.75},
  URN =		{urn:nbn:de:0030-drops-170136},
  doi =		{10.4230/LIPIcs.ESA.2022.75},
  annote =	{Keywords: Average Sensitivity, Knapsack Problem, FPRAS}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.18
Interval Query Problem on Cube-Free Median Graphs

Authors: Soh Kumabe

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
In this paper, we introduce the interval query problem on cube-free median graphs. Let G be a cube-free median graph and 𝒮 be a commutative semigroup. For each vertex v in G, we are given an element p(v) in 𝒮. For each query, we are given two vertices u,v in G and asked to calculate the sum of p(z) over all vertices z belonging to a u-v shortest path. This is a common generalization of range query problems on trees and grids. In this paper, we provide an algorithm to answer each interval query in O(log² n) time. The required data structure is constructed in O(n log³ n) time and O(n log² n) space. To obtain our algorithm, we introduce a new technique, named the staircases decomposition, to decompose an interval of cube-free median graphs into simpler substructures.
Cite as

Soh Kumabe. Interval Query Problem on Cube-Free Median Graphs. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kumabe:LIPIcs.ISAAC.2021.18,
  author =	{Kumabe, Soh},
  title =	{{Interval Query Problem on Cube-Free Median Graphs}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{18:1--18:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.18},
  URN =		{urn:nbn:de:0030-drops-154510},
  doi =		{10.4230/LIPIcs.ISAAC.2021.18},
  annote =	{Keywords: Data Structures, Range Query Problems, Median Graphs}
}
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