Computational Combinatorial Physics by Harmonizing Matroid Theory and Quantum Physics

• Project/Area Number: 16K12392
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Theory of informatics
• Research Institution: The University of Tokyo
• Principal Investigator: IMAI Hiroshi 東京大学, 大学院情報理工学系研究科, 教授 (80183010)
• Research Collaborator: Moriyama Sonoko 日本大学, 文理学部情報科学科, 教授 ; Hiraishi Hidefumi 東京大学, 情報理工学系研究科コンピュータ科学専攻, 助教
• Project Period (FY): 2016-04-01 – 2019-03-31
• Project Status: Completed (Fiscal Year 2018)
• Budget Amount: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000); Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: アルゴリズム / 固定パラメタ容易性 / 点モデル / Pottsモデル / Tutte多項式 / グラフ向き付け / 組合せ物理 / Iceモデル / 6点モデル / マトロイド / グラフ / アルゴリズム論 / マトロイドマイナー理論 / アルゴリズム理論

Outline of Final Research Achievements

This research aimed at harmonzing matroid theory and combinatorial physics to analyze combinatorial and physical problems by developing efficient algorithm for their computational analyses. We devised FPT algorithms for computing the partition function of ice-type mode with respect to the carving width of a target underlying graph. We also developed an FPT algorithm to evaluate the partition function of Potts mode. Concerning the Merino-Welsh conjecture on the Tutte polynomial, related to Lieb's square ice constant, we preformed computational analyses, and obtain counterexamples to its variant.

Academic Significance and Societal Importance of the Research Achievements

従来、数理物理において数学と物理の両面から研究されてきた組合せ物理において、計算解析を行うアルゴリズムの開発と、本研究グループメンバが構築した組合せ構造のデータベースを活用した解析を行うことによって、新たに計算論的組合せ物理という研究アプローチを示した。融合する諸分野の理論予想の一部解決も行え、アルゴリズム論からはFPTアルゴリズムの有用性を広げた。物理モデルの量子情報処理との関係を通した量子コンピュータへ研究を展開することが期待できる。

Research Products

• [Int'l Joint Research] ETH Zurich(スイス)
• [Journal Article] Smallest Counterexamples for Convexity and Log-concavity of the Tutte Polynomial (2019)
  • Author(s): Hidefumi Hiraishi, Hiroshi Imai, Sonoko Moriyama, Shuma Okamura, and Shinya Shiroshita
  • Journal Title: The 11th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications Volume: -
  • Peer Reviewed
• [Journal Article] Revisiting the Top-Down Computation of BDD of Spanning Trees of a Graph and Its Tutte Polynomial (2019)
  • Author(s): F. S. Oliveira, H. Hiraishi, and H. Imai
  • Journal Title: IEICE Trans. Fundamentals Volume: 印刷中
  • NAID: 130007699447
  • Peer Reviewed / Open Access
• [Journal Article] FPT Algorithms to Enumerate and Count Acyclic and Totally Cyclic Orientations (2019)
  • Author(s): F. S. Oliveira, H. Hiraishi, and H. Imai
  • Journal Title: The X Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS 2019) Volume: -
  • Peer Reviewed
• [Journal Article] Parameterized Algorithms to Compute Ising Partition Function (2018)
  • Author(s): Hidefumi Hiraishi and Sonoko Moriyama:
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E101.A Issue: 9 Pages: 1398-1403
  • DOI: 10.1587/transfun.E101.A.1398
  • NAID: 130007479457
  • ISSN: 0916-8508, 1745-1337
  • Year and Date: 2018-09-01
  • Peer Reviewed
• [Journal Article] A BDD Approach to Counting Problems in Graphic Arrangements (2018)
  • Author(s): F. S. Oliveira, H. Hiraishi, H. Imai
  • Journal Title: The 21st Japan-Korea Joint Workshop on Algorithms and Computation (WAAC 2018) Volume: -
  • Peer Reviewed
• [Journal Article] Parameterized Algorithm to Compute the Partition Function of Potts Model with Branch Decomposition (2018)
  • Author(s): Naosuke Shindo, Hidefumi Hiraishi and Hiroshi Imai
  • Journal Title: The 21st Japan-Korea Joint Workshop on Algorithms and Computation (WAAC 2018) Volume: -
  • Peer Reviewed
• [Journal Article] FPT Algorithms Exploiting Carving Decomposition for Eulerian Orientations and Ice-Type Models (2018)
  • Author(s): S. Shiroshita, T. Ogasawara, H. Hiraishi, H. Imai
  • Journal Title: Lecture Notes in Computer Science (WALCOM 2018) Volume: 10755 Pages: 216-227
  • DOI: 10.1007/978-3-319-75172-6_19
  • ISBN: 9783319751719, 9783319751726
  • Peer Reviewed
• [Journal Article] Parametrized Algorithms to Compute Ising Partition Function (2018)
  • Author(s): H. Hiraishi, H. Imai, Y. Iwata, B. Lin
  • Journal Title: IEICE Trans. Fundamentals Volume: -
  • Peer Reviewed
• [Journal Article] Comparing Simulated Annealing with Simulated Quantum Annealing on Max-cut and Other NP-Hard Problems (2018)
  • Author(s): H. Chang, H. Hiraishi, H. Imai
  • Journal Title: 17th Asian Quantum Information Science Conference Volume: -
  • Peer Reviewed
• [Journal Article] An FPT Algorithm for Counting the Number of Eulerian Orientations Exploiting Carving Decomposition (2017)
  • Author(s): S. Shiroshita, T. Ogasawara, H. Hiraishi, H.Imai
  • Journal Title: Proceedings of the 20th Korea-Japan Joint Workshop on Algorithms and Computation (WAAC 2017) Volume: Session 3:4
  • Peer Reviewed
• [Journal Article] Experimental Evaluation of Annealing Metaheuristics for NP-hard Problems (2017)
  • Author(s): H. Chang, H. Hiraishi, H. Imai
  • Journal Title: Proceedings of the 20th Korea-Japan Joint Workshop on Algorithms and Computation (WAAC 2017) Volume: Session 4:2
• [Journal Article] A Lower Bound on Opaque Sets (2016)
  • Author(s): Akitoshi Kawamura, Sonoko Moriyama, Yota Otachi, Janos Pach
  • Journal Title: Proc. of the 32nd Symposium on Computational Geometry Volume: 32
  • DOI: 10.4230/LIPIcs.SoCG.2016.46
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Parametric multiroute flow and its application to multilink-attack network (2016)
  • Author(s): Jean-Francois Baffier, Vorapong Suppakitpaisarn, Hidefumi Hiraishi and Hiroshi Imai
  • Journal Title: Discrete Optimization Volume: 22 Pages: 20-36
  • DOI: 10.1016/j.disopt.2016.05.002
  • Peer Reviewed
• [Presentation] Graph Orientations and Their Use in Modelling the Physical Sciences (2019)
  • Author(s): F. S. Oliveira, H. Hiraishi, and H. Imai
  • Organizer: 3rd ETH Zurich-UTokyo Strategic Partnership Symposium on the UN Sustainable Development Goals and Innovation
  • Int'l Joint Research
• [Presentation] Simulated Quantum AnnealingとBreakout Local SearchのNP-hard問題に対する実験的な比較 (2019)
  • Author(s): 寺西 寛人, 今井 浩, 平石 秀史
  • Organizer: 情報処理学会第172回アルゴリズム研究会
• [Presentation] Parameterized Algorithms for Tutte Polynomial Specializations in Graph Orientations (2019)
  • Author(s): F. S. Oliveira, H. Hiraishi, H. Imai
  • Organizer: 情報処理学会第172回アルゴリズム研究会
• [Presentation] 最大カット問題と量子計算 --- 常識の「嘘」も考えながら (2018)
  • Author(s): 今井浩
  • Organizer: 日本OR学会最適化とその応用研究部会未来を担う若手研究者の集い 2018
  • Invited
• [Presentation] Simulated Quantum Annealing versus Breakout Local Search for Benchmark Dataset on NP-hard Problems (2018)
  • Author(s): K. Teranishi, H. Imai, H, Hiraishi
  • Organizer: Asian Quantum Information Science Conference (AQIS 2018)
  • Int'l Joint Research
• [Presentation] Geometry and Quantum Computing (2017)
  • Author(s): Hidefumi Hiraishi
  • Organizer: ETH Zurich-UTokyo Strategic Partnership Symposium on Science, Design, Manufacturing and Information
  • Place of Presentation: 東京大学、東京都
  • Year and Date: 2017-01-20
• [Presentation] 制限付きボルツマンマシンに対する経路積分モンテカルロ法の実験的評価 (2017)
  • Author(s): 張 亨碩, 橋本 朔弥, 平石 秀史, 今井 浩
  • Organizer: 人工知能基本問題研究会
• [Presentation] A Note on Extended Formulations of Lower-truncated Transversal Polymatroids (2016)
  • Author(s): Hidefumi Hiraishi, Hiroshi Imai
  • Organizer: The fifth International Conference on Continuous Optimization
  • Place of Presentation: 政策研究大学院大学, 東京都
  • Year and Date: 2016-08-11
• [Presentation] Geometric Optimization Related with an LCP with SPD-matrices (2016)
  • Author(s): Sonoko Moriyama, Bernd Gaertner, Hiroshi Imai and Hiroyuki Miyazawa
  • Organizer: The fifth International Conference on Continuous Optimization
  • Place of Presentation: 政策研究大学院大学, 東京都
  • Year and Date: 2016-08-11
• [Presentation] Q[x]-representable Excluded Minors for Q-Representable Matroids of Rank Three (2016)
  • Author(s): Hidefumi Hiraishi, Sonoko Moriyama
  • Organizer: 2016 International Workshop on Structure in Graphs and Matroids
  • Place of Presentation: Eindhoven, Netherlands
  • Year and Date: 2016-07-25
  • Invited
• [Presentation] 媒介中心性に基づくシャプレイ値の高速近似計算アルゴリズム (2016)
  • Author(s): 上里晃平、大坂直人、平石秀史
  • Organizer: 夏のLAシンポジウム
  • Place of Presentation: かんぽの宿大和平群, 奈良県
  • Year and Date: 2016-07-20
• [Presentation] Excluded Minors for Matroids of Rank Three (2016)
  • Author(s): Sonoko Moriyama, Hidefumi Hiraishi
  • Organizer: SIAM on Conference on Discrete Mathematics
  • Place of Presentation: Atlanta, USA
  • Year and Date: 2016-06-06
  • Int'l Joint Research / Invited