分散並列計算と逐次計算における計算限界導出技法の融合と深化

• Project Area: A multifaceted approach toward understanding the limitations of computation
• Project/Area Number: 15H00852
• Research Category: Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)
• Allocation Type: Single-year Grants
• Review Section: Science and Engineering
• Research Institution: Nagoya Institute of Technology
• Principal Investigator: 泉 泰介 名古屋工業大学, 工学(系)研究科(研究院), 准教授 (20432461)
• Project Period (FY): 2015-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2016: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2015: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
• Keywords: 分散アルゴリズム / グラフアルゴリズム / 通信複雑性 / アルゴリズム / 分散システム / 計算量理論 / グラフ理論 / 個体群プロトコル

Outline of Annual Research Achievements

計算機ネットワーク上の効率的な計算、協調を目的としたアルゴリズムは分散・並列アルゴリズムと呼ばれ、種々の特徴的な要因によりその計算複雑性の理論は、逐次計算における複雑性理論とは異なる形で発展を遂げてきた。本研究では，両者をより高次な視点から俯瞰し、共通の困難性を見いだすという側面から検討を行い，研究を遂行した．特にグラフ上の諸問題に対して，グラフマイナー理論，量子計算，情報理論等の関連他分野におけるテクニックを積極的に分散アルゴリズムの設計に生かすことで，いくつかの課題において既存の限界を打破する成果を得た．特に，低競合ショートカットに関する研究，グラフ上の三角形発見に関する研究は，当該分野におけるトップ会議へと採択され，高い評価を得た．具体的には以下の通りである．
- 木構造低競合ショートカットの汎用的な構成方法の提案：低競合ショートカットはラウティング手法の一種であり，分散グラフアルゴリズムにおいて重要な応用を持つ．本研究では木構造から生じる低競合ショートカットを発見する，汎用的な分散アルゴリズムを示した．提案アルゴリズムは任意のグラフに対して適用可能な初めてのアルゴリズムである．また，部分k木や種数制限グラフ等，これまでに存在，構成法等が知られていないかったグラフクラスに対して効率的なショートカットを構成可能であることを示した．
- CONGESTネットワークモデルにおける三角形探索と列挙：分散グラフアルゴリズムの標準的なモデルの一つであるCONGESTモデルにおいて，世界で初めて三角形の発見および列挙を準線形時間で行う分散アルゴリズムを示した．また，同問題に対する初めての非自明な計算時間下界を示した．本成果は量子計算，情報理論等のテクニックを駆使しており，新学術領域における連携研究の成果として意義が深いものである．

Research Progress Status

28年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

28年度が最終年度であるため、記入しない。

Research Products

• [Int'l Joint Research] カーネギーメロン大学/ニューメキシコ大学(米国)
• [Int'l Joint Research] カーネギーメロン大学(米国)
• [Journal Article] Triangle Finding and Listing in CONGEST networks (2017)
  • Author(s): T. Izumi, F. Le Gall
  • Journal Title: Proc. of ACM Sumposium on Princples of Distributed Computing Volume: -
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Improving the lower bound on opaque sets for equilateral triangle (2016)
  • Author(s): Taisuke Izumi
  • Journal Title: Discrete Applied Mathematics Volume: 213 Pages: 130-138
  • DOI: 10.1016/j.dam.2016.05.006
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Bitwise MAP Estimation for Group Testing Based on Holographic Transformation (2016)
  • Author(s): Tadashi Wadayama, Taisuke Izumi, Kazushi Mimura
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: 99-A Pages: 2147-2154
  • NAID: 130005170498
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Low-Congestion Shortcuts without Embedding (2016)
  • Author(s): Bernhard Haeupler, Taisuke Izumi, Goran Zuzic
  • Journal Title: Proc. of ACM Sumposium on Princples of Distributed Computing Volume: - Pages: 451-460
  • DOI: 10.1145/2933057.2933112
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Bounds on asymptotic rate of capacitive crosstalk avoidance codes for on-chip buses (2016)
  • Author(s): Tadashi Wadayama, Taisuke Izumi
  • Journal Title: Proc. of International Symposium on Information Theory Volume: - Pages: 400-404
  • DOI: 10.1109/isit.2016.7541329
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Near-Optimal Low-Congestion Shortcuts on Bounded Parameter Graphs (2016)
  • Author(s): Bernhard Haeupler, Taisuke Izumi, Goran Zuzic
  • Journal Title: Proc. of International Symposium on Distributed Computing Volume: - Pages: 158-172
  • DOI: 10.1007/978-3-662-53426-7_12
  • ISBN: 9783662534250, 9783662534267
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Low-Congestion Shortcuts without Embedding (2016)
  • Author(s): Bernhard Haeupler, Taisuke Izumi and Goran Zuzic
  • Journal Title: Proc. of The 35th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC) Volume: なし
• [Journal Article] Listing Center Strings Under the Edit Distance Metric (2015)
  • Author(s): Hiromitsu Maji, Taisuke Izumi
  • Journal Title: Proc. of International Conference on Combinatorial Optimization and Applications Volume: LNCS9486 Pages: 771-782
  • DOI: 10.1007/978-3-319-26626-8_57
  • ISBN: 9783319266251, 9783319266268
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Approximability of Minimum Certificate Dispersal with Tree Structures (2015)
  • Author(s): Ta. Izumi, To. Izumi, H. Ono, K. Wada
  • Journal Title: Theoretical Computer Science Volume: 591 Pages: 5-14
  • DOI: 10.1016/j.tcs.2015.01.007
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] On Space and Time Complexity of Loosely-Stabilizing Leader Election (2015)
  • Author(s): Taisuke Izumi
  • Journal Title: Proc. of 22nd International Colloquium on Structural Information and Communication Complexity (SIROCCO) Volume: LNCS9439 Pages: 299-312
  • DOI: 10.1007/978-3-319-25258-2_21
  • ISBN: 9783319252575, 9783319252582
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Subgraph Domatic Problem and Writing Capacity of Devices with Restricted State Transitions (2015)
  • Author(s): Tadashi Wadayama, Taisuke Izumi, Hirotaka Ono
  • Journal Title: Proc. of IEEE International Symposum on Information Theory (ISIT) Volume: なし Pages: 1307-1311
  • DOI: 10.1109/isit.2015.7282667
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Bitwise MAP Estimation for Group Testing Based on Holographic Transformation (2015)
  • Author(s): Tadashi Wadayama, Taisuke Izumi, Kazushi Mimura
  • Journal Title: Proc. of IEEE International Symposium on Information Theory (ISIT) Volume: なし Pages: 2787-2791
  • DOI: 10.1109/isit.2015.7282964
  • NAID: 130005170498
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Triangle Finding and Listing in CONGEST networks (2017)
  • Author(s): F. Le Gall
  • Organizer: ACM Sumposium on Princples of Distributed Computing
  • Place of Presentation: ワシントンDC, 米国
  • Year and Date: 2017-07-25
  • Int'l Joint Research
• [Presentation] Near-Optimal Low-Congestion Shortcuts on Bounded Parameter Graphs (2016)
  • Author(s): Taisuke Izumi
  • Organizer: International Symposium on Distributed Computing
  • Place of Presentation: パリ，フランス
  • Year and Date: 2016-09-27
  • Int'l Joint Research
• [Presentation] Low-Congestion Shortcuts without Embedding (2016)
  • Author(s): Goran Zuzic
  • Organizer: ACM Sumposium on Princples of Distributed Computing
  • Place of Presentation: シカゴ，米国
  • Year and Date: 2016-07-25
  • Int'l Joint Research
• [Presentation] Bounds on asymptotic rate of capacitive crosstalk avoidance codes for on-chip buses (2016)
  • Author(s): Tadashi Wadayama
  • Organizer: International Symposium on Information Theory
  • Place of Presentation: バルセロナ，スペイン
  • Year and Date: 2016-07-10
  • Int'l Joint Research
• [Presentation] Toward Time-Optimal Gathering for Mobile Robots with Limited Visibility (2016)
  • Author(s): Taisuke Izumi
  • Organizer: 6th Research Meeting on Distributed Computing by Mobile Robots
  • Place of Presentation: パリ，フランス
  • Int'l Joint Research / Invited
• [Presentation] 通信複雑性入門 (2015)
  • Author(s): 泉 泰介
  • Organizer: 電子情報通信学会IT研究会
  • Place of Presentation: 岡山県倉敷市
  • Year and Date: 2015-11-24
  • Invited
• [Presentation] Local Algorithms for Mobile Robots: From Solvability to Complexiity (2015)
  • Author(s): Taisuke Izumi
  • Organizer: DISC2015 Workshop on Distributed Robotic Swarms
  • Place of Presentation: 東京都千代田区
  • Year and Date: 2015-10-05
  • Invited
• [Presentation] Improving lower bound on opaque set for regular triangle (2015)
  • Author(s): Taisuke Izumi
  • Organizer: The 18th Japan Conference on Discrete and Computational Geometry and Graphs
  • Place of Presentation: 京都府京都市
  • Year and Date: 2015-09-14
  • Int'l Joint Research