6 Search Results for "Maezawa, Shun-ichi"

Document
DOI: 10.4230/LIPIcs.SoCG.2026.16
Flip Distance of Non-Crossing Spanning Trees: NP-Hardness and Improved Bounds

Authors: Håvard Bakke Bjerkevik, Joseph Dorfer, Linda Kleist, Torsten Ueckerdt, and Birgit Vogtenhuber

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

Abstract
We consider the problem of reconfiguring non-crossing spanning trees on point sets. For a set P of n points in general position in the plane, the flip graph ℱ(P) has a vertex for each non-crossing spanning tree on P and an edge between any two spanning trees that can be transformed into each other by the exchange of a single edge (coined a flip). This flip graph has been intensively studied, lately with an emphasis on determining its diameter diam(ℱ(P)) for sets P of n points in convex position. For this case, the current best bounds are 14/9⋅n - O(1) ≤ diam(ℱ(P)) < 15/9⋅n - 3, obtained in a recent breakthrough work [Bjerkevik, Kleist, Ueckerdt, and Vogtenhuber; SODA 2025]. The crucial tool for both the upper and lower bound are so-called conflict graphs, which the authors stated might be the key ingredient for determining the diameter (up to lower-order terms). In this paper, we pick up the concept of conflict graphs from the above-mentioned work and show that this tool is even more versatile than previously hoped. As our first main result, we use conflict graphs to show that computing the flip distance between two non-crossing spanning trees is NP-hard, even for point sets in convex position. Interestingly, the result still holds for more constrained flip operations, concretely, compatible flips (where the removed and the added edge do not cross) and rotations (where the removed and the added edge share an endpoint). Additionally, we present new insights on the diameter of the flip graph, by this directly extending the line of research from [BKUV SODA25]. Their lower bound is based on a constant-size pair of trees, one of which is of a type we refer to as stacked. We show that if one of the trees is stacked, then the lower bound is indeed optimal up to a constant term, that is, there exists a flip sequence of length at most 14/9⋅(n-1) to any other tree. Lastly, we improve the lower bound on the diameter of the flip graph ℱ(P) for n points in convex position to 11/7⋅n-o(n).
Cite as

Håvard Bakke Bjerkevik, Joseph Dorfer, Linda Kleist, Torsten Ueckerdt, and Birgit Vogtenhuber. Flip Distance of Non-Crossing Spanning Trees: NP-Hardness and Improved Bounds. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bjerkevik_et_al:LIPIcs.SoCG.2026.16,
  author =	{Bjerkevik, H\r{a}vard Bakke and Dorfer, Joseph and Kleist, Linda and Ueckerdt, Torsten and Vogtenhuber, Birgit},
  title =	{{Flip Distance of Non-Crossing Spanning Trees: NP-Hardness and Improved Bounds}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{16:1--16:18},
  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.2026.16},
  URN =		{urn:nbn:de:0030-drops-258225},
  doi =		{10.4230/LIPIcs.SoCG.2026.16},
  annote =	{Keywords: Non-crossing, spanning tree, plane graph, flip graph, reconfiguration, diameter, complexity, NP-hard, edge exchange, compatible flip, rotation, happy edge property}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.63
Computing Distances on Graph Associahedra Is Fixed-Parameter Tractable

Authors: Luís Felipe I. Cunha, Ignasi Sau, Uéverton S. Souza, and Mario Valencia-Pabon

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

Abstract
An elimination tree of a connected graph G is a rooted tree on the vertices of G obtained by choosing a root v and recursing on the connected components of G-v to obtain the subtrees of v. The graph associahedron of G is a polytope whose vertices correspond to elimination trees of G and whose edges correspond to tree rotations, a natural operation between elimination trees. These objects generalize associahedra, which correspond to the case where G is a path. Ito et al. [ICALP 2023] recently proved that the problem of computing distances on graph associahedra is NP-hard. In this paper we prove that the problem, for a general graph G, is fixed-parameter tractable parameterized by the distance k. Prior to our work, only the case where G is a path was known to be fixed-parameter tractable. To prove our result, we use a novel approach based on a marking scheme that restricts the search to a set of vertices whose size is bounded by a (large) function of k.
Cite as

Luís Felipe I. Cunha, Ignasi Sau, Uéverton S. Souza, and Mario Valencia-Pabon. Computing Distances on Graph Associahedra Is Fixed-Parameter Tractable. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 63:1-63:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cunha_et_al:LIPIcs.ICALP.2025.63,
  author =	{Cunha, Lu{\'\i}s Felipe I. and Sau, Ignasi and Souza, U\'{e}verton S. and Valencia-Pabon, Mario},
  title =	{{Computing Distances on Graph Associahedra Is Fixed-Parameter Tractable}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{63:1--63:19},
  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.2025.63},
  URN =		{urn:nbn:de:0030-drops-234408},
  doi =		{10.4230/LIPIcs.ICALP.2025.63},
  annote =	{Keywords: graph associahedra, elimination tree, rotation distance, parameterized complexity, fixed-parameter tractable algorithm, combinatorial shortest path, reconfiguration}
}
Document
DOI: 10.4230/LIPIcs.SAND.2024.10
On the Complexity of Temporal Arborescence Reconfiguration

Authors: Riccardo Dondi and Manuel Lafond

Published in: LIPIcs, Volume 292, 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)

Abstract
We analyze the complexity of Arborescence Reconfiguration on temporal digraphs (Temporal Arborescence Reconfiguration). The problem, given two temporal arborescences in a temporal digraph, asks for the minimum number of arc flips, i.e. arc exchanges, that result in a sequence of temporal arborescences that transforms one into the other. We analyze the complexity of the problem, taking into account also its approximation and parameterized complexity, even in restricted cases. First, we solve an open problem showing that Temporal Arborescence Reconfiguration is NP-hard for two timestamps. Then we show that even if the two temporal arborescences differ only by two arcs, then the problem is not approximable within factor bln|V(D)|, for any constant 0 < b < 1, where V(D) is the set of vertices of the temporal arborescences. Finally, we prove that Temporal Arborescence Reconfiguration is W[1]-hard when parameterized by the number of arc flips needed to transform one temporal arborescence into the other.
Cite as

Riccardo Dondi and Manuel Lafond. On the Complexity of Temporal Arborescence Reconfiguration. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dondi_et_al:LIPIcs.SAND.2024.10,
  author =	{Dondi, Riccardo and Lafond, Manuel},
  title =	{{On the Complexity of Temporal Arborescence Reconfiguration}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{10:1--10:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.10},
  URN =		{urn:nbn:de:0030-drops-198888},
  doi =		{10.4230/LIPIcs.SAND.2024.10},
  annote =	{Keywords: Arborescence, Temporal Graphs, Graph Algorithms, Parameterized Complexity, Approximation Complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.81
Rerouting Planar Curves and Disjoint Paths

Authors: Takehiro Ito, Yuni Iwamasa, Naonori Kakimura, Yusuke Kobayashi, Shun-ichi Maezawa, Yuta Nozaki, Yoshio Okamoto, and Kenta Ozeki

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

Abstract
In this paper, we consider a transformation of k disjoint paths in a graph. For a graph and a pair of k disjoint paths 𝒫 and 𝒬 connecting the same set of terminal pairs, we aim to determine whether 𝒫 can be transformed to 𝒬 by repeatedly replacing one path with another path so that the intermediates are also k disjoint paths. The problem is called Disjoint Paths Reconfiguration. We first show that Disjoint Paths Reconfiguration is PSPACE-complete even when k = 2. On the other hand, we prove that, when the graph is embedded on a plane and all paths in 𝒫 and 𝒬 connect the boundaries of two faces, Disjoint Paths Reconfiguration can be solved in polynomial time. The algorithm is based on a topological characterization for rerouting curves on a plane using the algebraic intersection number. We also consider a transformation of disjoint s-t paths as a variant. We show that the disjoint s-t paths reconfiguration problem in planar graphs can be determined in polynomial time, while the problem is PSPACE-complete in general.
Cite as

Takehiro Ito, Yuni Iwamasa, Naonori Kakimura, Yusuke Kobayashi, Shun-ichi Maezawa, Yuta Nozaki, Yoshio Okamoto, and Kenta Ozeki. Rerouting Planar Curves and Disjoint Paths. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 81:1-81:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ito_et_al:LIPIcs.ICALP.2023.81,
  author =	{Ito, Takehiro and Iwamasa, Yuni and Kakimura, Naonori and Kobayashi, Yusuke and Maezawa, Shun-ichi and Nozaki, Yuta and Okamoto, Yoshio and Ozeki, Kenta},
  title =	{{Rerouting Planar Curves and Disjoint Paths}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{81:1--81:19},
  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.2023.81},
  URN =		{urn:nbn:de:0030-drops-181339},
  doi =		{10.4230/LIPIcs.ICALP.2023.81},
  annote =	{Keywords: Disjoint paths, combinatorial reconfiguration, planar graphs}
}
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.SoCG.2023.43
Reconfiguration of Colorings in Triangulations of the Sphere

Authors: Takehiro Ito, Yuni Iwamasa, Yusuke Kobayashi, Shun-ichi Maezawa, Yuta Nozaki, Yoshio Okamoto, and Kenta Ozeki

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
In 1973, Fisk proved that any 4-coloring of a 3-colorable triangulation of the 2-sphere can be obtained from any 3-coloring by a sequence of Kempe-changes. On the other hand, in the case where we are only allowed to recolor a single vertex in each step, which is a special case of a Kempe-change, there exists a 4-coloring that cannot be obtained from any 3-coloring. In this paper, we present a linear-time checkable characterization of a 4-coloring of a 3-colorable triangulation of the 2-sphere that can be obtained from a 3-coloring by a sequence of recoloring operations at single vertices. In addition, we develop a quadratic-time algorithm to find such a recoloring sequence if it exists; our proof implies that we can always obtain a quadratic length recoloring sequence. We also present a linear-time checkable criterion for a 3-colorable triangulation of the 2-sphere that all 4-colorings can be obtained from a 3-coloring by such a sequence. Moreover, we consider a high-dimensional setting. As a natural generalization of our first result, we obtain a polynomial-time checkable characterization of a k-coloring of a (k-1)-colorable triangulation of the (k-2)-sphere that can be obtained from a (k-1)-coloring by a sequence of recoloring operations at single vertices and the corresponding algorithmic result. Furthermore, we show that the problem of deciding whether, for given two (k+1)-colorings of a (k-1)-colorable triangulation of the (k-2)-sphere, one can be obtained from the other by such a sequence is PSPACE-complete for any fixed k ≥ 4. Our results above can be rephrased as new results on the computational problems named k-Recoloring and Connectedness of k-Coloring Reconfiguration Graph, which are fundamental problems in the field of combinatorial reconfiguration.
Cite as

Takehiro Ito, Yuni Iwamasa, Yusuke Kobayashi, Shun-ichi Maezawa, Yuta Nozaki, Yoshio Okamoto, and Kenta Ozeki. Reconfiguration of Colorings in Triangulations of the Sphere. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ito_et_al:LIPIcs.SoCG.2023.43,
  author =	{Ito, Takehiro and Iwamasa, Yuni and Kobayashi, Yusuke and Maezawa, Shun-ichi and Nozaki, Yuta and Okamoto, Yoshio and Ozeki, Kenta},
  title =	{{Reconfiguration of Colorings in Triangulations of the Sphere}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{43:1--43:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.43},
  URN =		{urn:nbn:de:0030-drops-178936},
  doi =		{10.4230/LIPIcs.SoCG.2023.43},
  annote =	{Keywords: Graph coloring, Triangulation of the sphere, Combinatorial reconfiguration}
}
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