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2020 年度 実績報告書

Using Containment Relations to Understand and Compute Width Parameters of Graphs

研究課題

研究課題/領域番号 18K11157
研究機関電気通信大学

研究代表者

BELMONTE Remy  電気通信大学, 大学院情報理工学研究科, 助教 (80780147)

研究期間 (年度) 2018-04-01 – 2021-03-31
キーワードParameterized algorithms / Graphs / Width parameters
研究実績の概要

As a result of this project, we have obtained a wide variety of algorithmic, complexity theoretic and graph theoretic results, in particular from the point of view of parameterized complexity and width parameters. Some highlights of the results obtained during the project include solving the computation complexity of the Independent Set Reconfiguration problem for the token sliding rule on split graph, which was a long-standing open problem, and identifying the first problem that distinguishes treewidth from path-width from the point of view of parameterized tractability, namely Grundy coloring. Together, the results we obtained help refine understanding of the complexity landscape of various fundamental graph-theoretic computational problems, especially from the point of view of width-parameters. We also obtained other various results, such as an in-depth study of the classical and parameterized complexity of finding large odd subgraphs and odd colorings of graphs. In particular, we studied the parameterized complexity of such problems under the graphs parameter rank-width, and proved that those problems can be solved in single-exponential time when parameterized by rank-width, the first problems shown to have this property. This distinguise those problems from their classical, non-parity variants, which, as far as current knowledge goes, require super-exponential running-time to be solved. We hope these results will pave the way to a better understanding of the differences between rank-width and clique-width (a parameter closely related to rank-width).

  • 研究成果

    (7件)

すべて 2020

すべて 雑誌論文 (4件) (うち国際共著 3件、 査読あり 3件) 学会発表 (3件)

  • [雑誌論文] Independent Set Reconfiguration Parameterized by Modular-Width2020

    • 著者名/発表者名
      Belmonte Remy、Hanaka Tesshu、Lampis Michael、Ono Hirotaka、Otachi Yota
    • 雑誌名

      Algorithmica

      巻: 82 ページ: 2586~2605

    • DOI

      https://doi.org/10.1007/s00453-020-00700-y

    • 査読あり / 国際共著
  • [雑誌論文] K_3 Edge Cover Problem in a Wide Sense2020

    • 著者名/発表者名
      Chiba Kyohei、Belmonte Remy、Ito Hiro、Lampis Michael、Nagao Atsuki、Otachi Yota
    • 雑誌名

      Journal of Information Processing

      巻: 28 ページ: 849~858

    • DOI

      https://doi.org/10.2197/ipsjjip.28.849

    • 査読あり / 国際共著
  • [雑誌論文] Parameterized (Approximate) Defective Coloring2020

    • 著者名/発表者名
      Belmonte Remy、Lampis Michael、Mitsou Valia
    • 雑誌名

      SIAM Journal on Discrete Mathematics

      巻: 34 ページ: 1084~1106

    • DOI

      https://doi.org/10.1137/18M1223666

    • 査読あり / 国際共著
  • [雑誌論文] Parameterized Complexity of Safe Set2020

    • 著者名/発表者名
      Belmonte Remy、Hanaka Tesshu、Katsikarelis Ioannis、Lampis Michael、Ono Hirotaka、Otachi Yota
    • 雑誌名

      Journal of Graph Algorithms and Applications

      巻: 24 ページ: 215~245

    • DOI

      https://doi.org/10.7155/jgaa.00528

  • [学会発表] On the Complexity of Finding Large Odd Induced Subgraphs and Odd Colorings2020

    • 著者名/発表者名
      Ignasi Sau
    • 学会等名
      WG 2020
  • [学会発表] Parameterized Complexity of (A, l)-Path Packing2020

    • 著者名/発表者名
      Yota Otachi
    • 学会等名
      IWOCA 2020
  • [学会発表] Grundy Distinguishes Treewidth from Pathwidth2020

    • 著者名/発表者名
      Michael Lampis
    • 学会等名
      ESA 2020

URL: 

公開日: 2021-12-27  

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