Study on Theory of Combinatorial Optimization with Applications to Robust Network Design

• Project/Area Number: 16K16010
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical informatics
• Research Institution: Kyoto University (2018-2019); University of Tsukuba (2016-2017)
• Principal Investigator: Kobayashi Yusuke 京都大学, 数理解析研究所, 准教授 (40581591)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 組合せ最適化 / アルゴリズム / グラフ / グラフアルゴリズム

Outline of Final Research Achievements

In this study, we developed a theory of combinatorial optimization problems arising in the context of robust network design. We dealt with generalized problems that are not dependent on a specific network or a specific situation. We designed efficient algorithms for many combinatorial optimization problems and analyzed their performance. In particular, we gave a first polynomial-time algorithm for the weighted linear matroid parity problem, which had been open for more than 30 years.

Academic Significance and Societal Importance of the Research Achievements

本研究では，様々な組合せ最適化問題に対して効率的アルゴリズムを与えた．扱った問題はいずれも一般性の高い問題であるため，現実のネットワーク設計への応用に役立つと考えられる．また，本研究で解決した重み付き線形マトロイドパリティ問題は，30年以上未解決だった問題であり，この問題に対して初の多項式時間アルゴリズムを与えたことは，理論研究において大きな意義のある成果である．

Research Products

• [Int'l Joint Research] ドルトムント工科大学(ドイツ)
• [Int'l Joint Research] グルノーブル大学/リヨン大学(フランス)
• [Int'l Joint Research] エトヴェシュ・ロラーンド大学(ハンガリー)
• [Int'l Joint Research] Eotvos University(ハンガリー)
• [Int'l Joint Research] Eotvos University(Hungary)
• [Journal Article] Shortest reconfiguration of colorings under Kempe-changes (2020)
  • Author(s): Marthe Bonamy, Marc Heinrich, Takehiro Ito, Yusuke Kobayashi, Haruka Mizuta, Moritz Muhlenthaler, Akira Suzuki, and Kunihiro Wasa
  • Journal Title: Proceedings of STACS 2020 Volume: -
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] An FPT algorithm for minimum additive spanner problem (2020)
  • Author(s): Yusuke Kobayashi
  • Journal Title: Proceedings of STACS 2020 Volume: -
  • Peer Reviewed / Open Access
• [Journal Article] A strongly polynomial time algorithm for the maximum supply rate problem on trees (2020)
  • Author(s): Takayama Koki、Kobayashi Yusuke
  • Journal Title: Theoretical Computer Science Volume: 806 Pages: 323-331
  • DOI: 10.1016/j.tcs.2019.05.014
  • Peer Reviewed / Open Access
• [Journal Article] Linear min-max relation between the treewidth of an H-minor-free graph and its largest grid minor (2020)
  • Author(s): Ken-ichi Kawarabayashi and Yusuke Kobayashi
  • Journal Title: Journal of Combinatorial Theory, Series B Volume: 141 Pages: 165-180
  • DOI: 10.1016/j.jctb.2019.07.007
  • Peer Reviewed / Open Access
• [Journal Article] An Improved Fixed-Parameter Algorithm for Max-Cut Parameterized by Crossing Number (2019)
  • Author(s): Kobayashi Yasuaki、Kobayashi Yusuke、Miyazaki Shuichi、Tamaki Suguru
  • Journal Title: Proceedings of the 30th International Workshop on Combinatorial Algorithms (IWOCA 2019) Volume: 30 Pages: 327-338
  • DOI: 10.1007/978-3-030-25005-8_27
  • ISBN: 9783030250041, 9783030250058
  • Peer Reviewed / Open Access
• [Journal Article] Diameter of colorings under Kempe changes (2019)
  • Author(s): Bonamy Marthe、Heinrich Marc、Ito Takehiro、Kobayashi Yusuke、Mizuta Haruka、Muehlenthaler Moritz、Suzuki Akira、Wasa Kunihiro
  • Journal Title: Proc. of COCOON 2019, Lecture Notes in Computer Science Volume: 11653 Pages: 52-64
  • DOI: 10.1007/978-3-030-26176-4_5
  • ISBN: 9783030261757, 9783030261764
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] The perfect matching reconfiguration problem (2019)
  • Author(s): Marthe Bonamy, Nicolas Bousquet, Marc Heinrich, Takehiro Ito, Yusuke Kobayashi, Arnaud Mary, Moritz Muhlenthaler, and Kunihiro Wasa
  • Journal Title: Proceedings of MFCS 2019 Volume: -
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Shortest reconfiguration of perfect matchings via alternating cycles (2019)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, and Yoshio Okamoto
  • Journal Title: Proceedings of ESA 2019 Volume: -
  • Peer Reviewed / Open Access
• [Journal Article] Parameterized algorithms for maximum cut with connectivity constraints (2019)
  • Author(s): Hiroshi Eto, Tesshu Hanaka, Yasuaki Kobayashi, and Yusuke Kobayashi
  • Journal Title: Proceedings of IWOCA 2019 Volume: -
  • Peer Reviewed / Open Access
• [Journal Article] Improved analysis of highest-degree branching for feedback vertex set (2019)
  • Author(s): Yoichi Iwata and Yusuke Kobayashi
  • Journal Title: Proceedings of IWOCA 2019 Volume: -
  • Peer Reviewed / Open Access
• [Journal Article] Two disjoint shortest paths problem with non-negative edge length (2019)
  • Author(s): Kobayashi Yusuke、Sako Ryo
  • Journal Title: Operations Research Letters Volume: 47 Issue: 1 Pages: 66-69
  • DOI: 10.1016/j.orl.2018.11.012
  • NAID: 120006769191
  • Peer Reviewed / Open Access
• [Journal Article] NP-hardness and fixed-parameter tractability of the minimum spanner problem (2018)
  • Author(s): Kobayashi Yusuke
  • Journal Title: Theoretical Computer Science Volume: 746 Pages: 88-97
  • DOI: 10.1016/j.tcs.2018.06.031
  • NAID: 120006769192
  • Peer Reviewed / Open Access
• [Journal Article] Reconfiguration of maximum-weight b-matchings in a graph (2018)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, and Yoshio Okamoto
  • Journal Title: Journal of Combinatorial Optimization Volume: 37 Issue: 2 Pages: 454-464
  • DOI: 10.1007/s10878-018-0289-3
  • NAID: 120006960832
  • Peer Reviewed / Open Access
• [Journal Article] A Strongly Polynomial Time Algorithm for the Maximum Supply Rate Problem on Trees (2018)
  • Author(s): Takayama Koki、Kobayashi Yusuke
  • Journal Title: Proceedings of the 12th International Frontiers of Algorithmics Workshop (FAW 2018) Volume: - Pages: 54-67
  • DOI: 10.1007/978-3-319-78455-7_5
  • ISBN: 9783319784540, 9783319784557
  • Peer Reviewed / Open Access
• [Journal Article] All-or-Nothing Multicommodity Flow Problem with Bounded Fractionality in Planar Graphs (2018)
  • Author(s): Kawarabayashi Ken-ichi、Kobayashi Yusuke
  • Journal Title: SIAM Journal on Computing Volume: 47 Issue: 4 Pages: 1483-1504
  • DOI: 10.1137/130932326
  • Peer Reviewed / Open Access
• [Journal Article] Tight approximability of the server allocation problem for real-time applications (2018)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto, and Taichi Shiitada
  • Journal Title: Proceedings of 3rd International Workshop on Algorithmic Aspects of Cloud Computing (ALGOCLOUD 2017) Volume: --- Pages: 41-55
  • DOI: 10.1007/978-3-319-74875-7_4
  • NAID: 120006998850
  • ISBN: 9783319748740, 9783319748757
  • Peer Reviewed / Open Access
• [Journal Article] Reconfiguration of Maximum-Weight b-Matchings in a Graph (2017)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, and Yoshio Okamoto
  • Journal Title: Proceedings of 23rd Annual International Computing and Combinatorics Conference (COCOON 2017) Volume: --- Pages: 287-296
  • DOI: 10.1007/978-3-319-62389-4_24
  • NAID: 120006960832
  • ISBN: 9783319623887, 9783319623894
  • Peer Reviewed / Open Access
• [Journal Article] The Directed Disjoint Shortest Paths Problem (2017)
  • Author(s): Kristof Berczi and Yusuke Kobayashi
  • Journal Title: Proceedings of the 25th European Symposium on Algorithms (ESA 2017) Volume: -
  • DOI: 10.4230/LIPIcs.ESA.2017.13
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Complexity of the Multi-Service Center Problem (2017)
  • Author(s): Ito Takehiro、Kakimura Naonori、Kobayashi Yusuke
  • Journal Title: Leibniz International Proceedings in Informatics Volume: 92
  • DOI: 10.4230/LIPIcs.ISAAC.2017.48
  • Peer Reviewed / Open Access
• [Journal Article] A weighted linear matroid parity algorithm (2017)
  • Author(s): Iwata Satoru、Kobayashi Yusuke
  • Journal Title: Proceedings of the 49th ACM Symposium on Theory of Computing (STOC 2017) Volume: - Pages: 264-276
  • DOI: 10.1145/3055399.3055436
  • Peer Reviewed / Open Access
• [Journal Article] Covering intersecting bi-set families under matroid constraints (2016)
  • Author(s): Kristof Berczi, Tamas Kiraly, and Yusuke Kobayashi
  • Journal Title: SIAM Journal on Discrete Mathematics Volume: 30 Issue: 3 Pages: 1758-1774
  • DOI: 10.1137/15m1049099
  • NAID: 120007129312
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] An Improved Approximation Algorithm for the Edge-Disjoint Paths Problem with Congestion Two (2016)
  • Author(s): Ken-ichi Kawarabayashi, Yusuke Kobayashi
  • Journal Title: ACM Trans. Algorithms Volume: 13 Issue: 1 Pages: 1-17
  • DOI: 10.1145/2960410
  • NAID: 120007135027
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] An FPT algorithm for minimum additive spanner problem (2020)
  • Author(s): Yusuke Kobayashi
  • Organizer: 37th Symposium on Theoretical Aspects of Computer Science (STACS 2020)
  • Int'l Joint Research
• [Presentation] Restricted 2-matching problems (2020)
  • Author(s): Yusuke Kobayashi
  • Organizer: International Workshop on Combinatorial Optimization and Algorithmic Game Theory
  • Int'l Joint Research / Invited
• [Presentation] Algorithms for gerrymandering over graphs (2019)
  • Author(s): Takehiro Ito, Naoyuki Kamiyama, Yusuke Kobayashi, and Yoshio Okamoto
  • Organizer: 18th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2019)
  • Int'l Joint Research
• [Presentation] 最小スパナー問題の困難性と固定パラメータ容易性 (2018)
  • Author(s): 小林佑輔
  • Organizer: 応用数理学会年会
• [Presentation] A weighted linear matroid parity algorithm (2018)
  • Author(s): 小林佑輔
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Invited
• [Presentation] A weighted linear matroid parity algorithm (2018)
  • Author(s): Yusuke Kobayashi
  • Organizer: HIM Follow-up WS to TP Combinatorial Optimization
  • Int'l Joint Research
• [Presentation] Weighted linear matroid parity problem (2017)
  • Author(s): Yusuke Kobayashi
  • Organizer: The 10th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications
  • Int'l Joint Research / Invited
• [Presentation] A weighted linear matroid parity algorithm (2017)
  • Author(s): Yusuke Kobayashi
  • Organizer: Franco-Japanese Days on Combinatorics and Optmization 2017 in Honour of Michel Deza
  • Int'l Joint Research / Invited
• [Presentation] 需給ネットワーク分割問題における供給率最大化アルゴリズム (2017)
  • Author(s): 高山 功輝, 小林 佑輔
  • Organizer: 日本応用数理学会2017年研究部会連合発表会
  • Place of Presentation: 電気通信大学（東京都調布市）
• [Remarks] Publications of Yusuke Kobayashi
  • URL: http://www.kurims.kyoto-u.ac.jp/~yusuke/research.html
• [Remarks] 小林 佑輔 (Yusuke KOBAYASHI)
  • URL: http://www.kurims.kyoto-u.ac.jp/~yusuke/
• [Remarks] Publications of Yusuke Kobayashi
  • URL: http://www.kurims.kyoto-u.ac.jp/~yusuke/talks.html
• [Remarks] Publications of Yusuke Kobayashi
  • URL: http://infoshako.sk.tsukuba.ac.jp/~kobayashi/research.html