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Research on Algorithms for Discrete Optimization Problems with Dynamic and On-Line Environments.

Research Project

Project/Area Number 05452122
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field Engineering fundamentals
Research InstitutionUniversity of Tokyo

Principal Investigator

IMAI Hiroshi  University of Tokyo, Graduate School of Science, Associate Professor, 大学院・理学系研究科, 助教授 (80183010)

Co-Investigator(Kenkyū-buntansha) IMAI Keiko  Chuo University, Faculty of Science and Engineering, Associate Professor, 理工学部, 助教授 (70203289)
Project Period (FY) 1993 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥6,400,000 (Direct Cost: ¥6,400,000)
Fiscal Year 1995: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1994: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1993: ¥3,200,000 (Direct Cost: ¥3,200,000)
KeywordsOn-line algorithm / Dynamic shortest paths / Dynamic computational geometry / Continuum algorithm / Real-time algorithm / 動的問題 / 実時間問題 / オンライン / 競合度 / 動的アルゴリズム / A^*アルゴリズム / ボロノイ図 / 計算幾何 / 線形計画法 / 並列ネットワーク / 分散システム
Research Abstract

The aim of this research is to develop efficient algorithms for discrete optimization problems under dynamic and on-line environments. Many practical problems have dynamic and on-line natures, and algorithms should be newly designed to handle dynamic and on-line factors.
First, we consider the dynamic shortest path problem where the distances of edges vary dynamically. This problem arises in real-time route navigation system where traffic jams makes the edge costs higher. We have developed A^*-based algorithms which make clever use of past solutions. Other techniques such as bidirectional search are also investigated. Also, to cope with future dynamic situations, a new algorithm to compute multiple candidates for route navigation in the given static environment is developed.
We formulate probelems of sharing information in distributed systems as an on-line model, and developed efficient on-line algorithms. The on-line nature is inherent in the distributed system, and we mainly consider page migration and replication probelms. To evaluate the on-line algorithms the so-called competitive ratio is used. Efficient algorithms in term of this ratio have been derived. Randomized techniques are demonstrated to be powerful for on-line problems.
Dynamic computational geometry is also investigated, especially the Voronoi diagram for dynamically moving points. The combinatorial complexity of dynamic Voronoi diagram is shown, together with its efficient construction algorithm. This is further applied to geometric clustering problem which have both discrete and continuous aspects. Randomized algorithms are developed by making use of these two aspects.
We have thus clarified fundamental structures of dynamic and on-line problems, and developed new paradigms to solve this new type of problems.

Report

(4 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • 1993 Annual Research Report
  • Research Products

    (32 results)

All Other

All Publications (32 results)

  • [Publications] S.Hasegawa,H,Imai and M.Ishiguro: "6-Appreximations of k-Label Spaces." Theoretical Computer Science. 137. 145-157 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Shibuya,T.Ikeda,H.Imai,S.Nishimura,H.Shimoura and K.Tenmoku: "Finding a Realistic Detour by AI Seavch Technidnes." Proceedings of the 2nd World Congress on Intelligent Transport Systems(ITS′95),Yokohama. 4. 2037-2044 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] S.Albers and H.Koga: "Page Migration with Limited Local Memory." Proceedings of the 4th International Workship on Algorithms and Data Structure(WADS'95),Lecture Notes in Computer Science. 955. 147-158 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Imai and M.Inaba: "Geometric Clustering with Applications." The Third International Congress on Industrial and Applied Mathematics(ICIAM'95).Book of Abstracts. 124-

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Shibuya: "Finding K Shortest Paths by AI Search Technidues." Cooperative Reseavch Repovt,“Optimization:Modeling and Algorithms."The Institute of Statistical Mathematics.77. 212-222 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 今井浩、今井桂子: "組合せ幾何学のアルゴリズム" 共立出版, (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] S.Hasegawa, H.Imai and M.Ishiguro: "E-Approximations of K-Label Spaces" Theoretical Computer Science. Vol. 137. 145-157 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Shibuya, T.Ikeda, H.Imai S.Nishimura, H.Shimoura and K.Tenmoku: "Finding a Realistic Detour by AI Search Techniques." Proceedings of the 2nd world Congress on Intelligent Transport Systems (ITS'95), Yokonama. vol.4. 2037-2044 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] S.Albers and H.Koga: "Page Migration with Limited Local Memory." Proceedings of the 4th International Workshop on Algorithms and Data Structure (WADS'95), Lecture Notes in Computer Science. vol.955. 147-158 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Imai and M.Inaba: "Geometric Clustering with Applications." The Third International Congress on Industrial and Applied Mathematics (ICIAM'95), Book of Abstracts. 124

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Shibuya, Finding K: "Shortest Paths by AI Serch Techniques" Cooperative Research Report, "Optimization Modeling and Algorithms, "The Institute of Statistical Mathematics.vol.77. 212-222 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Imai and K.Imai: Algorithms in Combinatrial Geometry. Kyoritsu, Tokyo, (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] S.Hasegawa,H.Imai and M.Isiguro: "ε-Approximations of k-Label Spaces." Theoretical COmputer Science.vol.137. 145-157 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] T.Shibuya,T,Ikeda,H.Imai,S.Nishimura,H.Shimoura and K.Tenmoku: "Finding a Realistic Detour by AI Search Technidues." Proceedings of the 2nd World Congress on Intelligent Trnsport Systems (ITS′95),Yokohama. vol.4. 2037-2044 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] S.Albers and H.Kaga: "Page Migration with Limited Local Memory." Proceedings of the 4th International Workshop on Algorithms and Data Structure(WADS′95),Lecture Notes in Computer Science. vol.955. 147-158 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] H.Imai and M.Inaba: "Geometric Clustering with Applications." The Third International Congress on Industrial and Applied Mathematics(ICIAM95),Book of Abstracts. 124

    • Related Report
      1995 Annual Research Report
  • [Publications] 今井 浩: "最適化とその周辺" 1995電子情報通信学会総合大会講演論文集、チュートリアル「今アルゴリズムの世界にこんな新しい流れが」. vol.1. 411-412 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] T.Shibuya: "Finding k Shortest Paths by AI Search Technidues." Cooperative Research Report,“Optimization:Modeling and Algorithms,"The Institute of Statistical Mathematics,. vol.77. 212-222 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 今井浩、今井桂子: "組合せ幾何学のアルゴリズム" 共立出版, (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] M.Inaba,N.Katoh and H.Imai: "Applications of Weighted Voronoi Diagrams and Randomization to Variance-Based k-Clustering" Proceedings of the 10th ACM Symposium on Computational Geometry. 332-339 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] S.Tani and H.Imai: "A Reordering Operation for an Ordered Binary Decision Diagram and an Extended Framework for Combinatorics of Graphs." Proceedings of the 5th International Symposium on Algorithms and Computation(ISAAC'94),Lecture Notes in Computer Science. Vol.834. 575-583 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] S.Albers and H.Koga: "New On-Line Algorithms for the Page Replication Problem." Proceedings of the 4th Scandinavian Workshop on Algorithm Theory,Lecture Notes in Computer Science. 25-36 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] T.Ono: "An Eight-Way Perturbation Technique for the Three-Dimensional Convex Hull." Proceedings of the 6th Canadian Conference on Computational Geometry. (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] M.-Y.Hsu,T.Ikeda,H.Imai,S.Nishimura 他: "A Fast Algorithm for Finding Better Routes by AI Search Techniques." Proceedings of the International Conference on Vehicle Navigation & Information Systems(VNIS'94). 291-296 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] D.Avis,今井浩,松永信介: "計算幾何学・離散幾何学" 朝倉書店, (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 今井浩、今井桂子: "計算幾何学" 共立出版, (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] M.Houle,H.Imai,K.Imai,J.-M.Robert and P.Yamamoto: "Orthogonal Weighted L_1 and L_∞ Approximation and Applications." Discrete Applied Mathematics. 43. 217-232 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] H.Imai: "Geometric Algorithms for Linear Programming" IEICE Transactions on Foundamentals. E76-A No.3. 259-264 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] H.Imai and T.Oomae: "Rounding a Real Vector to an Integral Vector in Integer Programming and its Porallelization." “Parallel Programming.Systems,"(C.K.Yuen and A.Yonezawa,eds),world Scientific. 218-222 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Y.Dai,H.Imai,K.Iwano and N.Katoh: "How to Treat Delete Requests in Semi-Online Problems." Lecture Notes in Computer Science. 762. 48-57 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 今井桂子・今井浩: "高次の動的Voronoi図とその応用" 情報処理学会論文誌. (掲載予定).

    • Related Report
      1993 Annual Research Report
  • [Publications] M.-Y.Hsu,H.Imai,et al.: "A fast algorithm for finding better routes by Al search techniques." International Conference on Vehicle Navigation and Information Systems. (発表予定). (1994)

    • Related Report
      1993 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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