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Similarities between the blocking and anti-blocking polyhedra

Research Project

Project/Area Number 26400185
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionYamagata University

Principal Investigator

Sakuma Tadashi  山形大学, 地域教育文化学部, 准教授 (60323458)

Co-Investigator(Kenkyū-buntansha) 柏原 賢二  東京大学, 大学院総合文化研究科, 助教 (70282514)
Co-Investigator(Renkei-kenkyūsha) HACHIMORI Masahiro  筑波大学, システム情報系, 准教授 (00344862)
NAKAMURA Masataka  東京大学, 大学院総合文化研究科, 准教授 (90155854)
Research Collaborator SHINOHARA Hidehiro  
Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
KeywordsIdeal clutter / Packing Property / MFMC Property / Tutte Polynomial / Chord Diagram / safe set / network majority / Packing and Covering / weighted sefe set / ブロッキング型整数多面体 / アンチブロッキング型整数多面体 / パッキングとカバリングの理論 / クラッター / packing property / MFMC-性 / 理想グラフ / near factorization / packing and covering / blocking polyhedra / anti-blocking polytope / perfect graph / ideal cullter / MFMC-property / 巡回群 / ideal clutter
Outline of Final Research Achievements

1): We give a scheme to attack the following conjecture proposed by Cornuejols, Guenin and Margot:"Every ideal minimally non-packing clutter has a transversal of size 2." Moreover, we show that the clutter of a combinatorial affine plane does not have any ideal minimally non-packing clutter of blocking number at least 3. 2): We prove that the chord expansion number equals the value of the Tutte polynomial at the point (2,-1) for its corresponding interlace graph. 3): A safe set of a graph G=(V,E) is a non-empty subset S of V such that for every component A of G[S] and every component B of G[V-S], we have |A|+1>|B| whenever there exists an edge of G between A and B. We give several graph theoretical properties of this concept. Furthermore we evaluate computational complexities of the problem of computing the minimum weight of a safe set on several graph classes.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (32 results)

All 2018 2017 2016 2015 2014 2013 Other

All Int'l Joint Research (15 results) Journal Article (12 results) (of which Int'l Joint Research: 5 results,  Peer Reviewed: 12 results,  Acknowledgement Compliant: 4 results) Presentation (3 results) (of which Int'l Joint Research: 2 results,  Invited: 2 results) Remarks (2 results)

  • [Int'l Joint Research] Universidad de Castilla-La Mancha(Spain)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] LRIUniversity Paris-Sud/LIAFAUniversity Paris-Diderot(France)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] MTA Renyi Institute/University of Pannonia(Hungary)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Shandong University(China)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Indian Statistical Institute(India)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research]

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Indian Statistical Institute(India)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] University Paris-Sud(France)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] Alfred Renyi Institute of Mathematics/University of Pannonia(Hungary)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] Ajou University(韓国)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] University of Victoria(Canada)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] Indian Statistical Institute(India)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] University Paris-Sud(France)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] Alfr´ed R´enyi Institute of Mathematics(Hungary)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] University of Victoria(Canada)

    • Related Report
      2015 Research-status Report
  • [Journal Article] On ideal minimally non-packing clutters2018

    • Author(s)
      Kenji Kashiwabara and Tadashi Sakuma
    • Journal Title

      Mathematical Programming and Game Theory (Springer research monograph)

      Volume: 印刷中

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Expansion of a Chord Diagram and the Tutte Polynomial2018

    • Author(s)
      Tomoki Nakamigawa and Tadashi Sakuma
    • Journal Title

      Discrete Mathematics

      Volume: 341 Issue: 6 Pages: 1573-1581

    • DOI

      10.1016/j.disc.2018.02.015

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Safe sets in graphs: Graph classes and structural parameters2018

    • Author(s)
      Raquel Agueda, Nathann Cohen, Shinya Fujita, Sylvain Legay, Yannis Manoussakis, Yasuko Matsui, Leandro Montero, Reza Naserasr, Hirotaka Ono, Yota Otachi, Tadashi Sakuma, Zsolt Tuza, Renyu Xu
    • Journal Title

      Journal of Combinatorial Optimization

      Volume: 印刷中 Issue: 4 Pages: 1221-1242

    • DOI

      10.1007/s10878-017-0205-2

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Safe sets, network majority on weighted trees2017

    • Author(s)
      Bapat Ravindra B.、Fujita Shinya、Legay Sylvain、Manoussakis Yannis、Matsui Yasuko、Sakuma Tadashi、Tuza Zsolt
    • Journal Title

      Networks

      Volume: 71 Issue: 1 Pages: 81-92

    • DOI

      10.1002/net.21794

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] The Expansion of a Chord Diagram and the Tutte Polynomial(extended abstract)2017

    • Author(s)
      T. Nakamigawa and T. Sakuma
    • Journal Title

      Electronic Notes in Discrete Mathematics

      Volume: 61 Pages: 917-923

    • DOI

      10.1016/j.endm.2017.07.054

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Safe set problem on graphs2016

    • Author(s)
      Shinya Fujita, Gary MacGillivray, Tadashi Sakuma
    • Journal Title

      Discrete Applied Mathematics

      Volume: 215 Pages: 106-111

    • DOI

      10.1016/j.dam.2016.07.020

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Network Majority on Tree Topological Network2016

    • Author(s)
      Ravindra B. Bapat, Shinya Fujita, Sylvain Legay, Yannis Manoussakis, Yasuko Matsui, Tadashi Sakuma, Zsolt Tuza.
    • Journal Title

      Electronic Notes in Discrete Mathematics

      Volume: 54 Pages: 79-84

    • DOI

      10.1016/j.endm.2016.09.015

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Safe Sets in Graphs: Graph Classes and Structural Parameters2016

    • Author(s)
      Raquel Agueda, Nathann Cohen, Shinya Fujita, Sylvain Legay, Yannis Manoussakis, Yasuko Matsui, Leandro Montero, Reza Naserasr, Yota Otachi, Tadashi Sakuma, Zsolt Tuza, Renyu Xu
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 10043 Pages: 241-253

    • DOI

      10.1007/978-3-319-48749-6_18

    • ISBN
      9783319487489, 9783319487496
    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On the Balanced Decomposition Number2015

    • Author(s)
      Tadashi SAKUMA
    • Journal Title

      Graphs and Combinatorics

      Volume: 31 Issue: 6 Pages: 2377-2380

    • DOI

      10.1007/s00373-015-1526-5

    • Related Report
      2015 Research-status Report 2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] An Accelerated Algorithm for Solving SVP Based on Statistical Analysis2015

    • Author(s)
      Masaharu Fukase, Kenji Kashiwabara
    • Journal Title

      Journal of Information Processing

      Volume: 23 Issue: 1 Pages: 67-80

    • DOI

      10.2197/ipsjjip.23.67

    • NAID

      130004952395

    • ISSN
      1882-6652
    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Safe set Problem on Graphs2014

    • Author(s)
      Shinya Fujita, Gary MacGillivray, Tadashi Sakuma
    • Journal Title

      The Proceedings of Bordeaux Graph Workshop 2014 Enseirb-Matmeca & LaBRI, Bordeaux, France, 19-22 November, 2014

      Volume: 1 Pages: 71-72

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Pebble exchange on graphs2013

    • Author(s)
      S. Fujita, T. Nakamigawa and T. Sakuma
    • Journal Title

      Discrete Applied Mathematics

      Volume: 184 Pages: 139-145

    • DOI

      10.1016/j.dam.2013.03.009

    • Related Report
      2015 Research-status Report 2014 Research-status Report
    • Peer Reviewed
  • [Presentation] Similarities and dissimilarities between the blocking and anti-blocking polyhedra2017

    • Author(s)
      Tadashi SAKUMA
    • Organizer
      2017 Symposium on Mathematical Programming and Game Theory (2017 SMPGT)
    • Place of Presentation
      Indian Statistical Institute, Delhi Centre
    • Year and Date
      2017-01-09
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Minimally non-ideal clutters and ideal minimally non-packing clutters2017

    • Author(s)
      Tadashi Sakuma
    • Organizer
      The 10th Anniversary Conference on Nonlinear Analysis and Convex Analysis
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] ブロッキング型及びアンチブロッキング型整数多面体の類似性について2016

    • Author(s)
      佐久間雅
    • Organizer
      日本数学会 2016年度年会 応用数学分科会 特別講演
    • Place of Presentation
      筑波大学
    • Year and Date
      2016-03-16
    • Related Report
      2015 Research-status Report
    • Invited
  • [Remarks] 研究者詳細

    • URL

      http://yudb.kj.yamagata-u.ac.jp/html/240_ronbn_1_ja.html

    • Related Report
      2017 Annual Research Report
  • [Remarks] 研究者詳細 佐久間雅

    • URL

      http://yudb.kj.yamagata-u.ac.jp/html/240_ronbn_ja.html

    • Related Report
      2014 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2022-02-16  

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