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Documents authored by Kamiyama, Naoyuki

Document
DOI: 10.4230/LIPIcs.ISAAC.2025.40
Minimum Sum Coloring with Bundles in Trees and Bipartite Graphs

Authors: Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, and Yoshio Okamoto

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

Abstract
The minimum sum coloring problem with bundles was introduced by Darbouy and Friggstad (SWAT 2024) as a common generalization of the minimum coloring problem and the minimum sum coloring problem. During their presentation, the following open problem was raised: whether the minimum sum coloring problem with bundles could be solved in polynomial time for trees. We answer their question in the negative by proving that the minimum sum coloring problem with bundles is NP-hard even for paths. We complement this hardness by providing algorithms of the following types. First, we provide a fixed-parameter algorithm for trees when the number of bundles is a parameter; this can be extended to graphs of bounded treewidth. Second, we provide a polynomial-time algorithm for trees when bundles form a partition of the vertex set and the difference between the number of vertices and the number of bundles is constant. Third, we provide a polynomial-time algorithm for trees when bundles form a partition of the vertex set and each bundle induces a connected subgraph. We further show that for bipartite graphs, the problem with weights is NP-hard even when the number of bundles is at least three, but is polynomial-time solvable when the number of bundles is at most two. The threshold shifts to three versus four for the problem without weights.
Cite as

Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, and Yoshio Okamoto. Minimum Sum Coloring with Bundles in Trees and Bipartite Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 40:1-40:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ito_et_al:LIPIcs.ISAAC.2025.40,
  author =	{Ito, Takehiro and Kakimura, Naonori and Kamiyama, Naoyuki and Kobayashi, Yusuke and Okamoto, Yoshio},
  title =	{{Minimum Sum Coloring with Bundles in Trees and Bipartite Graphs}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{40:1--40:14},
  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.2025.40},
  URN =		{urn:nbn:de:0030-drops-249482},
  doi =		{10.4230/LIPIcs.ISAAC.2025.40},
  annote =	{Keywords: graph algorithms, minimum sum coloring, minimum coloring, fixed-parameter tractability, NP-hardness}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.54
Reforming an Unfair Allocation by Exchanging Goods

Authors: Sheung Man Yuen, Ayumi Igarashi, Naoyuki Kamiyama, and Warut Suksompong

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

Abstract
Fairly allocating indivisible goods is a frequently occurring task in everyday life. Given an initial allocation of the goods, we consider the problem of reforming it via a sequence of exchanges to attain fairness in the form of envy-freeness up to one good (EF1). We present a vast array of results on the complexity of determining whether it is possible to reach an EF1 allocation from the initial allocation and, if so, the minimum number of exchanges required. In particular, we uncover several distinctions based on the number of agents involved and their utility functions. Furthermore, we derive essentially tight bounds on the worst-case number of exchanges needed to achieve EF1.
Cite as

Sheung Man Yuen, Ayumi Igarashi, Naoyuki Kamiyama, and Warut Suksompong. Reforming an Unfair Allocation by Exchanging Goods. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 54:1-54:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{yuen_et_al:LIPIcs.ISAAC.2025.54,
  author =	{Yuen, Sheung Man and Igarashi, Ayumi and Kamiyama, Naoyuki and Suksompong, Warut},
  title =	{{Reforming an Unfair Allocation by Exchanging Goods}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{54:1--54:21},
  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.2025.54},
  URN =		{urn:nbn:de:0030-drops-249626},
  doi =		{10.4230/LIPIcs.ISAAC.2025.54},
  annote =	{Keywords: fair division, indivisible goods, envy-freeness, exchanges}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.82
Hardness of Finding Combinatorial Shortest Paths on Graph Associahedra

Authors: Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Shun-ichi Maezawa, Yuta Nozaki, and Yoshio Okamoto

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
We prove that the computation of a combinatorial shortest path between two vertices of a graph associahedron, introduced by Carr and Devadoss, is NP-hard. This resolves an open problem raised by Cardinal. A graph associahedron is a generalization of the well-known associahedron. The associahedron is obtained as the graph associahedron of a path. It is a tantalizing and important open problem in theoretical computer science whether the computation of a combinatorial shortest path between two vertices of the associahedron can be done in polynomial time, which is identical to the computation of the flip distance between two triangulations of a convex polygon, and the rotation distance between two rooted binary trees. Our result shows that a certain generalized approach to tackling this open problem is not promising. As a corollary of our theorem, we prove that the computation of a combinatorial shortest path between two vertices of a polymatroid base polytope cannot be done in polynomial time unless P = NP. Since a combinatorial shortest path on the matroid base polytope can be computed in polynomial time, our result reveals an unexpected contrast between matroids and polymatroids.
Cite as

Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Shun-ichi Maezawa, Yuta Nozaki, and Yoshio Okamoto. Hardness of Finding Combinatorial Shortest Paths on Graph Associahedra. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 82:1-82:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ito_et_al:LIPIcs.ICALP.2023.82,
  author =	{Ito, Takehiro and Kakimura, Naonori and Kamiyama, Naoyuki and Kobayashi, Yusuke and Maezawa, Shun-ichi and Nozaki, Yuta and Okamoto, Yoshio},
  title =	{{Hardness of Finding Combinatorial Shortest Paths on Graph Associahedra}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{82:1--82:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel 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.2023.82},
  URN =		{urn:nbn:de:0030-drops-181344},
  doi =		{10.4230/LIPIcs.ICALP.2023.82},
  annote =	{Keywords: Graph associahedra, combinatorial shortest path, NP-hardness, polymatroids}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.61
Shortest Reconfiguration of Perfect Matchings via Alternating Cycles

Authors: Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, and Yoshio Okamoto

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
Motivated by adjacency in perfect matching polytopes, we study the shortest reconfiguration problem of perfect matchings via alternating cycles. Namely, we want to find a shortest sequence of perfect matchings which transforms one given perfect matching to another given perfect matching such that the symmetric difference of each pair of consecutive perfect matchings is a single cycle. The problem is equivalent to the combinatorial shortest path problem in perfect matching polytopes. We prove that the problem is NP-hard even when a given graph is planar or bipartite, but it can be solved in polynomial time when the graph is outerplanar.
Cite as

Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, and Yoshio Okamoto. Shortest Reconfiguration of Perfect Matchings via Alternating Cycles. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 61:1-61:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{ito_et_al:LIPIcs.ESA.2019.61,
  author =	{Ito, Takehiro and Kakimura, Naonori and Kamiyama, Naoyuki and Kobayashi, Yusuke and Okamoto, Yoshio},
  title =	{{Shortest Reconfiguration of Perfect Matchings via Alternating Cycles}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{61:1--61:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.61},
  URN =		{urn:nbn:de:0030-drops-111823},
  doi =		{10.4230/LIPIcs.ESA.2019.61},
  annote =	{Keywords: Matching, Combinatorial reconfiguration, Alternating cycles, Combinatorial shortest paths}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.11
On the Complexity of Stable Fractional Hypergraph Matching

Authors: Takashi Ishizuka and Naoyuki Kamiyama

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
In this paper, we consider the complexity of the problem of finding a stable fractional matching in a hypergraphic preference system. Aharoni and Fleiner proved that there exists a stable fractional matching in every hypergraphic preference system. Furthermore, Kintali, Poplawski, Rajaraman, Sundaram, and Teng proved that the problem of finding a stable fractional matching in a hypergraphic preference system is PPAD-complete. In this paper, we consider the complexity of the problem of finding a stable fractional matching in a hypergraphic preference system whose maximum degree is bounded by some constant. The proof by Kintali, Poplawski, Rajaraman, Sundaram, and Teng implies the PPAD-completeness of the problem of finding a stable fractional matching in a hypergraphic preference system whose maximum degree is 5. In this paper, we prove that (i) this problem is PPAD-complete even if the maximum degree is 3, and (ii) if the maximum degree is 2, then this problem can be solved in polynomial time. Furthermore, we prove that the problem of finding an approximate stable fractional matching in a hypergraphic preference system is PPAD-complete.
Cite as

Takashi Ishizuka and Naoyuki Kamiyama. On the Complexity of Stable Fractional Hypergraph Matching. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 11:1-11:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ishizuka_et_al:LIPIcs.ISAAC.2018.11,
  author =	{Ishizuka, Takashi and Kamiyama, Naoyuki},
  title =	{{On the Complexity of Stable Fractional Hypergraph Matching}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{11:1--11:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.11},
  URN =		{urn:nbn:de:0030-drops-99590},
  doi =		{10.4230/LIPIcs.ISAAC.2018.11},
  annote =	{Keywords: fractional hypergraph matching, stable matching, PPAD-completeness}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.12
The b-Branching Problem in Digraphs

Authors: Naonori Kakimura, Naoyuki Kamiyama, and Kenjiro Takazawa

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
In this paper, we introduce the concept of b-branchings in digraphs, which is a generalization of branchings serving as a counterpart of b-matchings. Here b is a positive integer vector on the vertex set of a digraph, and a b-branching is defined as a common independent set of two matroids defined by b: an arc set is a b-branching if it has at most b(v) arcs sharing the terminal vertex v, and it is an independent set of a certain sparsity matroid defined by b. We demonstrate that b-branchings yield an appropriate generalization of branchings by extending several classical results on branchings. We first present a multi-phase greedy algorithm for finding a maximum-weight b-branching. We then prove a packing theorem extending Edmonds' disjoint branchings theorem, and provide a strongly polynomial algorithm for finding optimal disjoint b-branchings. As a consequence of the packing theorem, we prove the integer decomposition property of the b-branching polytope. Finally, we deal with a further generalization in which a matroid constraint is imposed on the b(v) arcs sharing the terminal vertex v.
Cite as

Naonori Kakimura, Naoyuki Kamiyama, and Kenjiro Takazawa. The b-Branching Problem in Digraphs. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{kakimura_et_al:LIPIcs.MFCS.2018.12,
  author =	{Kakimura, Naonori and Kamiyama, Naoyuki and Takazawa, Kenjiro},
  title =	{{The b-Branching Problem in Digraphs}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{12:1--12:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.12},
  URN =		{urn:nbn:de:0030-drops-95948},
  doi =		{10.4230/LIPIcs.MFCS.2018.12},
  annote =	{Keywords: Greedy Algorithm, Packing, Matroid Intersection, Sparsity Matroid, Arborescence}
}
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