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Using Containment Relations to Understand and Compute Width Parameters of Graphs

Research Project

Project/Area Number 18K11157
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 60010:Theory of informatics-related
Research InstitutionThe University of Electro-Communications

Principal Investigator

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

Project Period (FY) 2018-04-01 – 2021-03-31
Project Status Discontinued (Fiscal Year 2020)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
KeywordsParameterized algorithms / Graphs / Width parameters / Reconfiguration / Parameterized complexity / Structural parameters / Algorithms / Containment relations
Outline of Annual Research Achievements

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).

Report

(3 results)
  • 2020 Annual Research Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (18 results)

All 2020 2019 Other

All Int'l Joint Research (4 results) Journal Article (6 results) (of which Int'l Joint Research: 6 results,  Peer Reviewed: 6 results,  Open Access: 5 results) Presentation (8 results) (of which Int'l Joint Research: 2 results)

  • [Int'l Joint Research] LAMSADE/Universite Paris Dauphine(フランス)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] LIRMM/Universite de Montpellier(フランス)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] LAMSADE/Universite Paris Dauphine(フランス)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] LIRMM/Universite de Montpellier/CNRS(フランス)

    • Related Report
      2018 Research-status Report
  • [Journal Article] Independent Set Reconfguration Parameterized by Modular-Width2020

    • Author(s)
      Remy Belmonte, Tesshu Hanaka, Michael Lampis, Hirotaka Ono, Yota Otachi
    • Journal Title

      Algorithmica

      Volume: - Issue: 9 Pages: 2586-2605

    • DOI

      10.1007/s00453-020-00700-y

    • Related Report
      2020 Annual Research Report 2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] <i>K</i><sub>3</sub> Edge Cover Problem in a Wide Sense2020

    • Author(s)
      Chiba Kyohei、Belmonte Remy、Ito Hiro、Lampis Michael、Nagao Atsuki、Otachi Yota
    • Journal Title

      Journal of Information Processing

      Volume: 28 Issue: 0 Pages: 849-858

    • DOI

      10.2197/ipsjjip.28.849

    • NAID

      130007956350

    • ISSN
      1882-6652
    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Parameterized (Approximate) Defective Coloring2020

    • Author(s)
      Belmonte Remy、Lampis Michael、Mitsou Valia
    • Journal Title

      SIAM Journal on Discrete Mathematics

      Volume: 34 Issue: 2 Pages: 1084-1106

    • DOI

      10.1137/18m1223666

    • Related Report
      2020 Annual Research Report 2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Parameterized Complexity of Safe Set2020

    • Author(s)
      Belmonte Remy、Hanaka Tesshu、Katsikarelis Ioannis、Lampis Michael、Ono Hirotaka、Otachi Yota
    • Journal Title

      Journal of Graph Algorithms and Applications

      Volume: 24 Issue: 3 Pages: 215-245

    • DOI

      10.7155/jgaa.00528

    • Related Report
      2020 Annual Research Report 2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Token Sliding on Split Graphs2020

    • Author(s)
      Belmonte Remy、Kim Eun Jung、Lampis Michael、Mitsou Valia、Otachi Yota、Sikora Florian
    • Journal Title

      Theory of Computing Systems

      Volume: Online Issue: 4 Pages: 662-686

    • DOI

      10.1007/s00224-020-09967-8

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] How Bad is the Freedom to Flood-It?2019

    • Author(s)
      Belmonte Remy、Khosravian Ghadikolaei Mehdi、Kiyomi Masashi、Lampis Michael、Otachi Yota
    • Journal Title

      Journal of Graph Algorithms and Applications

      Volume: 23 Issue: 2 Pages: 111-134

    • DOI

      10.7155/jgaa.00486

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] On the Complexity of Finding Large Odd Induced Subgraphs and Odd Colorings2020

    • Author(s)
      Ignasi Sau
    • Organizer
      WG 2020
    • Related Report
      2020 Annual Research Report
  • [Presentation] Parameterized Complexity of (A, l)-Path Packing2020

    • Author(s)
      Yota Otachi
    • Organizer
      IWOCA 2020
    • Related Report
      2020 Annual Research Report
  • [Presentation] Grundy Distinguishes Treewidth from Pathwidth2020

    • Author(s)
      Michael Lampis
    • Organizer
      ESA 2020
    • Related Report
      2020 Annual Research Report
  • [Presentation] On the complexity of finding large odd induced subgraphs and odd colorings2020

    • Author(s)
      Ignasi Sau
    • Organizer
      WG 2020
    • Related Report
      2019 Research-status Report
  • [Presentation] Parameterized Complexity of (A,l)-Path Packing2020

    • Author(s)
      Yota Otachi
    • Organizer
      IWOCA 2020
    • Related Report
      2019 Research-status Report
  • [Presentation] Independent Set Reconfiguration Parameterized by Modular-Width2019

    • Author(s)
      Remy Belmonte
    • Organizer
      WG 2019
    • Related Report
      2019 Research-status Report 2018 Research-status Report
  • [Presentation] Token sliding on split graphs2019

    • Author(s)
      Remy Belmonte
    • Organizer
      STACS 2019
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Parameterized Complexity of Safe Set2019

    • Author(s)
      Ioannis Katsikarelis
    • Organizer
      CIAC 2019
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research

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Published: 2018-04-23   Modified: 2021-12-27  

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