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Documents authored by Gima, Tatsuya

Document
DOI: 10.4230/LIPIcs.IPEC.2023.21
Bandwidth Parameterized by Cluster Vertex Deletion Number

Authors: Tatsuya Gima, Eun Jung Kim, Noleen Köhler, Nikolaos Melissinos, and Manolis Vasilakis

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

Abstract
Given a graph G and an integer b, Bandwidth asks whether there exists a bijection π from V(G) to {1, …, |V(G)|} such that max_{{u, v} ∈ E(G)} | π(u) - π(v) | ≤ b. This is a classical NP-complete problem, known to remain NP-complete even on very restricted classes of graphs, such as trees of maximum degree 3 and caterpillars of hair length 3. In the realm of parameterized complexity, these results imply that the problem remains NP-hard on graphs of bounded pathwidth, while it is additionally known to be W[1]-hard when parameterized by the treedepth of the input graph. In contrast, the problem does become FPT when parameterized by the vertex cover number of the input graph. In this paper, we make progress towards the parameterized (in)tractability of Bandwidth. We first show that it is FPT when parameterized by the cluster vertex deletion number cvd plus the clique number ω of the input graph, thus generalizing the previously mentioned result for vertex cover. On the other hand, we show that Bandwidth is W[1]-hard when parameterized only by cvd. Our results generalize some of the previous results and narrow some of the complexity gaps.
Cite as

Tatsuya Gima, Eun Jung Kim, Noleen Köhler, Nikolaos Melissinos, and Manolis Vasilakis. Bandwidth Parameterized by Cluster Vertex Deletion Number. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gima_et_al:LIPIcs.IPEC.2023.21,
  author =	{Gima, Tatsuya and Kim, Eun Jung and K\"{o}hler, Noleen and Melissinos, Nikolaos and Vasilakis, Manolis},
  title =	{{Bandwidth Parameterized by Cluster Vertex Deletion Number}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{21:1--21:15},
  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.2023.21},
  URN =		{urn:nbn:de:0030-drops-194401},
  doi =		{10.4230/LIPIcs.IPEC.2023.21},
  annote =	{Keywords: Bandwidth, Clique number, Cluster vertex deletion number, Parameterized complexity}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.20
Extended MSO Model Checking via Small Vertex Integrity

Authors: Tatsuya Gima and Yota Otachi

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
We study the model checking problem of an extended MSO with local and global cardinality constraints, called MSO^GL_Lin, introduced recently by Knop, Koutecký, Masařík, and Toufar [Log. Methods Comput. Sci., 15(4), 2019]. We show that the problem is fixed-parameter tractable parameterized by vertex integrity, where vertex integrity is a graph parameter standing between vertex cover number and treedepth. Our result thus narrows the gap between the fixed-parameter tractability parameterized by vertex cover number and the W[1]-hardness parameterized by treedepth.
Cite as

Tatsuya Gima and Yota Otachi. Extended MSO Model Checking via Small Vertex Integrity. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gima_et_al:LIPIcs.ISAAC.2022.20,
  author =	{Gima, Tatsuya and Otachi, Yota},
  title =	{{Extended MSO Model Checking via Small Vertex Integrity}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{20:1--20:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.20},
  URN =		{urn:nbn:de:0030-drops-173056},
  doi =		{10.4230/LIPIcs.ISAAC.2022.20},
  annote =	{Keywords: vertex integrity, monadic second-order logic, cardinality constraint, fixed-parameter tractability}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.61
Algorithmic Meta-Theorems for Combinatorial Reconfiguration Revisited

Authors: Tatsuya Gima, Takehiro Ito, Yasuaki Kobayashi, and Yota Otachi

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

Abstract
Given a graph and two vertex sets satisfying a certain feasibility condition, a reconfiguration problem asks whether we can reach one vertex set from the other by repeating prescribed modification steps while maintaining feasibility. In this setting, Mouawad et al. [IPEC 2014] presented an algorithmic meta-theorem for reconfiguration problems that says if the feasibility can be expressed in monadic second-order logic (MSO), then the problem is fixed-parameter tractable parameterized by treewidth + 𝓁, where 𝓁 is the number of steps allowed to reach the target set. On the other hand, it is shown by Wrochna [J. Comput. Syst. Sci. 2018] that if 𝓁 is not part of the parameter, then the problem is PSPACE-complete even on graphs of bounded bandwidth. In this paper, we present the first algorithmic meta-theorems for the case where 𝓁 is not part of the parameter, using some structural graph parameters incomparable with bandwidth. We show that if the feasibility is defined in MSO, then the reconfiguration problem under the so-called token jumping rule is fixed-parameter tractable parameterized by neighborhood diversity. We also show that the problem is fixed-parameter tractable parameterized by treedepth + k, where k is the size of sets being transformed. We finally complement the positive result for treedepth by showing that the problem is PSPACE-complete on forests of depth 3.
Cite as

Tatsuya Gima, Takehiro Ito, Yasuaki Kobayashi, and Yota Otachi. Algorithmic Meta-Theorems for Combinatorial Reconfiguration Revisited. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 61:1-61:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gima_et_al:LIPIcs.ESA.2022.61,
  author =	{Gima, Tatsuya and Ito, Takehiro and Kobayashi, Yasuaki and Otachi, Yota},
  title =	{{Algorithmic Meta-Theorems for Combinatorial Reconfiguration Revisited}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{61:1--61:15},
  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.2022.61},
  URN =		{urn:nbn:de:0030-drops-169991},
  doi =		{10.4230/LIPIcs.ESA.2022.61},
  annote =	{Keywords: Combinatorial reconfiguration, monadic second-order logic, fixed-parameter tractability, treedepth, neighborhood diversity}
}
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