分散計算複雑性の理論：最悪時評価を超えて

• Project Area: A multifaceted approach toward understanding the limitations of computation
• Project/Area Number: 25106507
• 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): 2013-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2014: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2013: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
• Keywords: 分散システム / アルゴリズム / 計算複雑性 / グラフ / 分散アルゴリズム / 計算量理論

Outline of Annual Research Achievements

多数の計算機を相互接続した分散システム上において動作するアルゴリズム（分散アルゴリズム）の設計においては、非同期性、局所性、故障耐性など特有の因子が関わってくる。これら特有の因子により，分散計算の複雑性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，特にこのような現状を鑑みて，分散計算と逐次計算の複雑性理論のより密接な関わりを見いだすことにより，両分野の垣根を越えた新たな結果を導き出すことを目指す，特に，近年逐次計算の分野において精力的に研究されている「最悪時ケースにおける計算限界」を超える新たな方法論を分散計算の計算限界解析に導入し，同分野の理論の深化を目指し研究を行なった．
代表的な成果としては「分散計算における距離問題の限界導出」および「分散計算と２者間通信複雑性理論の関連の理解」の２つを挙げることができる．前者の研究では，全点対最短経路問題を緩和した分散距離オラクルと呼ばれる問題に対し，計算時間と計算結果の精度の間に存在するトレードオフを明らかにし，その計算限界を導出した．後者の研究においては，計算機ネットワーク上の最小生成木問題，最短経路問題といった分散システムにおける代表的な問題に対して，2者間通信複雑性の理論を発展的に利用することで，決定性アルゴリズムに対する従来の結果を強化することに成功した．
その他，領域研究における分野間連携の結果として，省メモリスペースでの深さ優先探索アルゴリズム，単位円グラフにおける極大クリーク等の結果等を併せて得ることができた．また，分散計算分野における主要な国際会議の一つ(SIROCCO)を日本において本研究費のサポートのもと開催し，分野内における日本のコミュニティのプレゼンス向上に寄与した．

Research Progress Status

26年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

26年度が最終年度であるため、記入しない。

Research Products

• [Journal Article] Faster Enumeration of All Maximal Cliques in Unit Disk Graphs using Geometric Structure (2015)
  • Author(s): Taisuke Izumi, Daisuke Suzuki
  • Journal Title: IEICE Transactions on Information and Systems Volume: E98-D No.3 Pages: 490-496
  • NAID: 130004841866
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Approximability of Minimum Certificate Dispersal with Tree Structures (2015)
  • Author(s): Taisuke Izumi, Tomoko Izumi, Hirotaka Ono, Koichi Wada
  • Journal Title: Theoretical Computer Science Volume: 未定
  • Peer Reviewed
• [Journal Article] Space-efficient Self-stabilizing Counting Population Protocols on mobile sensor networks (2014)
  • Author(s): Tomoko Izumi, Keigo Kinpara, Taisuke Izumi, Koichi Wada
  • Journal Title: Theoretical Computer Science Volume: 552 Pages: 99-108
  • DOI: 10.1016/j.tcs.2014.07.028
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Filling Logarithmic Gaps in Distributed Complexity for Global Problems (2014)
  • Author(s): Hiroaki Ookawa, Taisuke Izumi
  • Journal Title: Lecture Notes in Computer Science Volume: 8939 Pages: 377-388
  • DOI: 10.1007/978-3-662-46078-8_31
  • ISBN: 9783662460771, 9783662460788
  • Peer Reviewed
• [Journal Article] Depth-First Search Using O(n) Bits (2014)
  • Author(s): Tetsuo Asano, Taisuke Izumi, Masashi Kiyomi, Matsuo Konagaya, Hirotaka Ono, Yota Otachi, Pascal Schweitzer, Jun Tarui, Ryuhei Uehara
  • Journal Title: Algorithms and Computation Lecture Notes in Computer Science Volume: 8889 Pages: 553-564
  • DOI: 10.1007/978-3-319-13075-0_44
  • ISBN: 9783319130743, 9783319130750
  • Peer Reviewed
• [Journal Article] Time Lower Bounds for Distributed Distance Oracles (2014)
  • Author(s): Taisuke Izumi, Roger Wattenhofer
  • Journal Title: Lecture Notes in Computer Science Volume: 8878 Pages: 60-75
  • DOI: 10.1007/978-3-319-14472-6_5
  • ISBN: 9783319144719, 9783319144726
  • Peer Reviewed
• [Journal Article] Randomized Lower Bound for Distributed Spanning-Tree Verification (2014)
  • Author(s): Taisuke Izumi
  • Journal Title: Lecture Notes in Computer Science Volume: 8576 Pages: 137-148
  • DOI: 10.1007/978-3-319-09620-9_12
  • ISBN: 9783319096193, 9783319096209
  • Peer Reviewed
• [Journal Article] On Complexity of Distributed Diameter Approximation (2014)
  • Author(s): Taisuke Izumi and Roger Wattenhofer
  • Journal Title: 電子情報通信学会コンピュテーション研究会 Volume: IEICE-COMP2013-69 Pages: 61-68
  • NAID: 110009861246
• [Journal Article] Feasibility of Polynomial-time Randomized Gathering for Oblivious Mobile Robots (2013)
  • Author(s): Taisuke Izumi, Tomoko Izumi, Sayaka Kamei, Fukuhito Oosita
  • Journal Title: IEEE Transactions on Parallel and Distributed Systems Volume: Vol. 24, No. 4 Issue: 4 Pages: 716-723
  • DOI: 10.1109/tpds.2012.212
  • Peer Reviewed
• [Journal Article] Scalable Estimation of Network Average Degree (2013)
  • Author(s): Taisuke Izumi and Hironobu Kanzaki
  • Journal Title: Lecture Notes in Computer Science Volume: 8255 Pages: 367-369
  • DOI: 10.1007/978-3-319-03089-0_32
  • ISBN: 9783319030883, 9783319030890
  • Peer Reviewed
• [Journal Article] On Enumerating All Maximal Cliques in Unit Disk Graphs (2013)
  • Author(s): Daisuke Suzuki and Taisuke Izumi
  • Journal Title: 電子情報通信学会コンピュテーション研究会 Volume: IEICE-COMP2013-40 Pages: 15-20
• [Journal Article] On Parallel Complexity of MapReduce Computation (2013)
  • Author(s): Koichi Wada and Taisuke Izumi
  • Journal Title: 電子情報通信学会コンピュテーション研究会 Volume: IEICE-COMP2013-17 Pages: 143-147
  • NAID: 110009768655
• [Presentation] Filling Logarithmic Gaps in Distributed Complexity for Global Problems (2015)
  • Author(s): Hiroaki Ookawa
  • Organizer: 41st International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM2015)
  • Place of Presentation: チェコ共和国
  • Year and Date: 2015-01-24 – 2015-01-29
• [Presentation] Time Lower Bounds for Distributed Distance Oracles (2014)
  • Author(s): Taisuke Izumi
  • Organizer: The 18th International Conference on Principles of Distributed Systems (OPODIS2014)
  • Place of Presentation: イタリア
  • Year and Date: 2014-12-16 – 2014-12-19
• [Presentation] Depth-First Search Using O(n) bits (2014)
  • Author(s): Matsuo Konagaya
  • Organizer: The 25th International Symposium on Algorithms and Computation (ISAAC)
  • Place of Presentation: 韓国
  • Year and Date: 2014-12-15 – 2014-12-17
• [Presentation] On the Worst-Case Initial Configuration for Conservative Connectivity Preservation (2014)
  • Author(s): Daichi Kaino
  • Organizer: SRDS Workshop on Self-organization in Swarm of Robots(WSSR)
  • Place of Presentation: 奈良，日本
  • Year and Date: 2014-10-06 – 2014-10-09
• [Presentation] Randomized Lower Bound for Distributed Spanning-Tree Verification (2014)
  • Author(s): Taisuke Izumi
  • Organizer: 21st International Colloquium on Structural Information and Communication Complexity (SIROCCO2014)
  • Place of Presentation: 高山，奈良
  • Year and Date: 2014-07-23 – 2014-07-25
• [Presentation] Enumerating All Maximal Cliques in Unit Disk Graphs (2014)
  • Author(s): Daisuke Suzuki and Taisuke Izumi
  • Organizer: 40th International Conference on Current Trends in Theory and Practice of Computer Science
  • Place of Presentation: ハイタトラス，スロバキア
• [Presentation] Scalable Estimation of Network Average Degree (2013)
  • Author(s): Taisuke Izumi and Hironobu Kanzaki
  • Organizer: 15th International Symposium on Stabilization, Safety, and Security of Distributed Systems
  • Place of Presentation: 大阪，日本