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アルゴリズム的グラフマイナー理論

Research Project

Project/Area Number 21650004
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeSingle-year Grants
Research Field Fundamental theory of informatics
Research InstitutionNational Institute of Informatics

Principal Investigator

河原林 健一  国立情報学研究所, 情報学プリンシプル研究系, 教授 (40361159)

Project Period (FY) 2009 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2010: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2009: ¥1,400,000 (Direct Cost: ¥1,400,000)
Keywordsグラフマイナー / アルゴリズム / 多項式時間 / 平面グラフ / 曲面上のグラフ / マイナー操作 / セパレイター / 最短パス / グラフ / マイナー / グラフマイナー理論 / 点素パス問題
Research Abstract

本年度は,主にセパレイターを研究した.1970年代にLIPTON-TARJANによって導入された平面グラフのセパレイターは,その後,グラフアルゴリズム分野の強力なツールとなった.例えば,平面ネットワーク上の最短パス問題などは,セパレイターの性質によるところが大きい
全てのグラフがセパレイターを持つとは限らない,例えば,Expanderグラフや,密なグラフなどは,セパレイターがないことが知られている.したがってセパレイターが存在するグラフ族はなにか?という問題が,過去30年間調べられている.そして近年になって,最終的には,マイナーに関して閉じているグラフ族がセパレイターをもつある種の「限界」のグラフ族だと結論付けられている
マイナーに関して閉じているグラフ族に関しては,Alon-Seymour-Thomasによる有名な結果(J.AMS&STOC'90)が知られている.彼らは,その論文の中で,具体的なセパレイターのサイズを予想した.この予想は,過去20年間でもセパレイターに関して最も注目された予想であり,いくつもの部分的結果が発表されてきた
2010年度,B.Reed氏との共同研究で,この予想を完全解決した.論文は,理論計算機分野で最も権威がある国際会議であるFOCS (Annual Symposium on Foundations of Computer Science)に採択され,この会議の特集号に招待された

Report

(2 results)
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (31 results)

All 2011 2010 2009 Other

All Journal Article (25 results) (of which Peer Reviewed: 25 results) Presentation (4 results) Remarks (2 results)

  • [Journal Article] Algorithms for finding an induced cycle in planar graphs2010

    • Author(s)
      K.Kawarabayashi, Y.Kobayashi
    • Journal Title

      Combinatorica

      Volume: 30 Pages: 715-734

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A separator theorem in minor-closed classes2010

    • Author(s)
      K.Kawarabayashi, B.Reed
    • Journal Title

      the 51st Annual Symposium on Foundations of Computer Science (FOCS'10)

      Volume: FOCS'10 Pages: 153-152

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A shorter proof of the Graph Minor Algorithm-The Unique Linkage Theorem-2010

    • Author(s)
      K.Kawarabayashi, P.Wollan
    • Journal Title

      42nd ACM Symposium on Theory of Computing (STOC'10)

      Volume: STOC'10 Pages: 687-694

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Recognizing a totally odd K4-subdivision, parity 2-disjoint rooted paths and a parity cycle through specified elements2010

    • Author(s)
      K.Kawarabayashi, et al.
    • Journal Title

      ACM-SIAM Symposium on Discrete Algorithms,(SODA'10)

      Pages: 318-328

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Decomposition, approximation, and coloring of odd-minor-free graphs2010

    • Author(s)
      E.Demaine, et al.
    • Journal Title

      ACM-SIAM Symposium on Discrete Algorithms,(SODA'10)

      Pages: 329-344

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The edge disjoint paths problem in Eulerian graphs and 4-edge-connected graphs2010

    • Author(s)
      K.Kawarabayashi, et al.
    • Journal Title

      ACM-SIAM Symposium on Discrete Algorithms,(SODA'10)

      Pages: 345-353

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An(almost)linear time algorithm for odd cycles transversal2010

    • Author(s)
      K.Kawarabayashi, et al.
    • Journal Title

      ACM-SIAM Symposium on Discrete Algorithms,(SODA'10)

      Pages: 365-378

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Acyclic coloring and Star coloring surfaces2010

    • Author(s)
      K.Kawarabayashi, et al.
    • Journal Title

      Siam J.Discrete Math. 24

      Pages: 56-71

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dominating sets in triangulations on surfaces2010

    • Author(s)
      T.Honjo, et al.
    • Journal Title

      J.Graph Theory 63

      Pages: 17-30

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Planarity allowing few error vertices in linear time2009

    • Author(s)
      K.Kawarabayashi
    • Journal Title

      50th Annual Symposium on Foundations of Computer Science(FOCS 2009)

      Pages: 639-648

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Note on nonseparating and removable cycles in highly connected graphs2009

    • Author(s)
      S.Fujita, et al.
    • Journal Title

      Discrete Applied Math 159

      Pages: 398-399

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A weakening of the odd Hadwiger's conjecture2009

    • Author(s)
      K.Kawarabayashi
    • Journal Title

      Combinatorics, Probability and Computing 17

      Pages: 815-821

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Long cycles without hamiltonian paths2009

    • Author(s)
      K.Kawarabayashi, et al.
    • Journal Title

      Discrete Math 308

      Pages: 5899-5906

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Highly parity linked graphs2009

    • Author(s)
      K.Kawarabayashi, et al.
    • Journal Title

      Combinatorica 29

      Pages: 215-225

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Approximation Algorithms via Structural Results for Apex-Minor-Free Graphs2009

    • Author(s)
      E.Demaine, et al.
    • Journal Title

      35th International Colloquium on Automata, Languages and Programming(ICALP'09)

      Pages: 316-327

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hadwiger's Conjecture is decidable2009

    • Author(s)
      K.Kawarabayashi, et al.
    • Journal Title

      the 41st ACM Symposium on Theory of Computing(STOC'09)

      Pages: 445-454

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Note on coloring graphs without odd Kk-minors2009

    • Author(s)
      K.Kawarabayashi
    • Journal Title

      J.Combin.Theory Ser.B 99

      Pages: 728-731

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Decomposing planar graphs of girth five into an independent set and a forest2009

    • Author(s)
      K.Kawarabayashi, et al.
    • Journal Title

      J.Combin.Theory Ser.B 99

      Pages: 674-684

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Algorithmic graph minor theory. Improved grid minor bounds and Wagner's contraction2009

    • Author(s)
      E.Demaine, et al.
    • Journal Title

      Algorithmica 54

      Pages: 142-180

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Linear connectivity forces large complete bipartite minors2009

    • Author(s)
      T.Bohme, et al.
    • Journal Title

      J.Combin.Theory Ser.B 99

      Pages: 557-582

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 6-critical graphs on the Klein bottle2009

    • Author(s)
      K.Kawarabayashi, et al.
    • Journal Title

      Siam J.Discrete Math 23

      Pages: 372-383

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] N-flips in even triangulations on a surface2009

    • Author(s)
      K.Kawarabayashi, et al.
    • Journal Title

      J.Combin.Theory Ser.B 99

      Pages: 229-246

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the number of 4-contractible edges in 4-connected graphs2009

    • Author(s)
      K.Ando, et al.
    • Journal Title

      J.Combin.Theory Ser.B 99

      Pages: 97-109

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Removable cycles in non-bipartite graphs2009

    • Author(s)
      K.Kawarabayashi, et al.
    • Journal Title

      J.Combin.Theory Ser.B 99

      Pages: 30-38

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] K_6-minor in triangulations in the Klein bottle2009

    • Author(s)
      K.Kawarabayashi, et al.
    • Journal Title

      Siam J.Discrete Math 23

      Pages: 96-108

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] The disjoint paths problem---Algorithm and Structure2011

    • Author(s)
      K.Kawarabayashi
    • Organizer
      WALCOM'2011
    • Place of Presentation
      IITニューデリー
    • Year and Date
      2011-02-20
    • Related Report
      2010 Annual Research Report
  • [Presentation] Graphs without subdivision2009

    • Author(s)
      K.Kawarabayashi
    • Organizer
      Danish Graph Theory
    • Place of Presentation
      Copenhagen
    • Year and Date
      2009-11-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] The disjoint paths problem, structure and algorithm2009

    • Author(s)
      K.Kawarabayashi
    • Organizer
      Fourth workshop in Graph Classes, Optimization, and Width Parameters, GROW 2009
    • Place of Presentation
      Bergen
    • Year and Date
      2009-10-15
    • Related Report
      2009 Annual Research Report
  • [Presentation] Hadwiger's conjecture is decidable2009

    • Author(s)
      K.Kawarabayashi
    • Organizer
      The 6th Japan-Hungary conference in Discrete Math
    • Place of Presentation
      Budapest
    • Year and Date
      2009-05-16
    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://research.nii.ac.jp/~k_keniti/

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://researchmap.jp/k_keniti/

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2009-04-01   Modified: 2016-04-21  

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