Similarities between the blocking and anti-blocking polyhedra

• Project/Area Number: 26400185
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Yamagata 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: ¥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)
• Keywords: Ideal 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.

Research Products

• [Int'l Joint Research] Universidad de Castilla-La Mancha(Spain)
• [Int'l Joint Research] LRIUniversity Paris-Sud/LIAFAUniversity Paris-Diderot(France)
• [Int'l Joint Research] MTA Renyi Institute/University of Pannonia(Hungary)
• [Int'l Joint Research] Shandong University(China)
• [Int'l Joint Research] Indian Statistical Institute(India)
• [Int'l Joint Research]
• [Int'l Joint Research] Indian Statistical Institute(India)
• [Int'l Joint Research] University Paris-Sud(France)
• [Int'l Joint Research] Alfred Renyi Institute of Mathematics/University of Pannonia(Hungary)
• [Int'l Joint Research] Ajou University(韓国)
• [Int'l Joint Research] University of Victoria(Canada)
• [Int'l Joint Research] Indian Statistical Institute(India)
• [Int'l Joint Research] University Paris-Sud(France)
• [Int'l Joint Research] Alfr´ed R´enyi Institute of Mathematics(Hungary)
• [Int'l Joint Research] University of Victoria(Canada)
• [Journal Article] On ideal minimally non-packing clutters (2018)
  • Author(s): Kenji Kashiwabara and Tadashi Sakuma
  • Journal Title: Mathematical Programming and Game Theory (Springer research monograph) Volume: 印刷中
  • Peer Reviewed
• [Journal Article] The Expansion of a Chord Diagram and the Tutte Polynomial (2018)
  • 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
  • Peer Reviewed
• [Journal Article] Safe sets in graphs: Graph classes and structural parameters (2018)
  • 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
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Safe sets, network majority on weighted trees (2017)
  • 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
  • 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
  • Peer Reviewed
• [Journal Article] Safe set problem on graphs (2016)
  • 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
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Network Majority on Tree Topological Network (2016)
  • 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
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Safe Sets in Graphs: Graph Classes and Structural Parameters (2016)
  • 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
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] On the Balanced Decomposition Number (2015)
  • Author(s): Tadashi SAKUMA
  • Journal Title: Graphs and Combinatorics Volume: 31 Issue: 6 Pages: 2377-2380
  • DOI: 10.1007/s00373-015-1526-5
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] An Accelerated Algorithm for Solving SVP Based on Statistical Analysis (2015)
  • 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
  • Peer Reviewed
• [Journal Article] Safe set Problem on Graphs (2014)
  • 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
  • Peer Reviewed
• [Journal Article] Pebble exchange on graphs (2013)
  • 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
  • Peer Reviewed
• [Presentation] Similarities and dissimilarities between the blocking and anti-blocking polyhedra (2017)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Minimally non-ideal clutters and ideal minimally non-packing clutters (2017)
  • Author(s): Tadashi Sakuma
  • Organizer: The 10th Anniversary Conference on Nonlinear Analysis and Convex Analysis
  • 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
  • Invited
• [Remarks] 研究者詳細
  • URL: http://yudb.kj.yamagata-u.ac.jp/html/240_ronbn_1_ja.html
• [Remarks] 研究者詳細 佐久間雅
  • URL: http://yudb.kj.yamagata-u.ac.jp/html/240_ronbn_ja.html