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Research on Vector and Parallel Processing of Computer Algebra Algorithms and Distributed and Cooperative Processing

Research Project

Project/Area Number 07680337
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 計算機科学
Research InstitutionThe University of Tokyo

Principal Investigator

MURAO Hirokazu  The University of Tokyo, Computer Center, Research Associate, 大型計算機センター, 助手 (60174265)

Project Period (FY) 1995 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1996: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1995: ¥1,800,000 (Direct Cost: ¥1,800,000)
Keywordscomputer algebra / parallel processing / polynomial factorization / integer GCD / algebraic equation system / asymptotically fast algorithm / polynomial interpolation / multipoint polynomial evaluation / 並列処理(タスク並列) / 整数GCD計算 / 並列アルゴリズム
Research Abstract

The overall subject of this research project is the application of vector and/or parallel processing to computational algebra. It is expected to enable us, by making full use of the superior computing power and rich resources of high-performance computers in symbolic and algebraic computation, to perform ultimate-scale symbolic calculations in practice. The following lists the brief descriptions of the major research results.
1. The latest algorithms for distinct degree factorization of polynomials over finite fields, which can be regarded as a break-down method for large-scale problems of polynomials with very high degrees, and their complexities are investigated very deeply. As its result, a simple method for improvement is found. Furthermore, by noticing the obvious algebraic independences in the algorithms, the investigator has developed a new algorithm for parallel processing, taking account of communication latency as well. The result of this work is presented at ISSAC'96 and publ … More iched in the proceedings.
2. The new algorithm for sparse multivariate polynomial interpolation, developed by the investigator a few years ago, was revisited and examined to make its description and analysis more complete. The paper of this work was published in the special issue on parallel symbolic computation of Journal of Symbolic Computation.
3. In recent yers, research on the classical problem of integer GCD calculation has been activated, aiming mainly at its parallel processing, and a few new algorithms are published. In this project, the investigator implemented some of those algorithms in Risa/Asir, to verify their much-improved performance. This implementation is further applied to the Grobner basis calculation for solving a system of algebraic equations, and we observed 6-8% reduction of computing time for solving a realistic large-scale problem. Furthermore, the research group of Risa/Asir has succeeded in computing a very large scale problem related with Grobner basis calculation, which have never veen completed till then in the world, using our new implementation and their thchnology of distributed processing. In their paper, it is reported that out new implementation, along with their idea for removal of integer contents from the intermediate polynomials, contributed very much to the success.
4. Nowadays, it has been becoming a common recognition that the use of the asymptotically fast algorithms for polynomial operations is practical and necessary when treating large scale polynomials. In this project, some of the algorithms are implemented empirically, to be used in the calculations listed here. Through this development and empirical study, the investigator has learned various implementation techniques for attaining practical efficiency.
5. By optimizing the exiting asymptotically fast algorithm, the investigator developed a new fast algorithm for polynomial multipoint evaluation, which is used in various polynomial calculations such as distinct degree factorization. At the same time, its parallelization, with communication latency being taken into account, is considered. A paper on this work is submitted and accepted for presentation at PASCO'97, and its implementation in KLIC for parallel processing is in progress.
As for distributed and cooperative processing, the minimal but sufficient functions of Risa/Asir, realized by the developer during the term of this project, are used, and no further dovelopment is done by the investigator, because he has recognized that further mathematical studies and development of parallel algorithms will be of much more importance, rather than the sofrware development at this point of time. Less

Report

(3 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • Research Products

    (26 results)

All Other

All Publications (26 results)

  • [Publications] 藤瀬,村尾: "並列DDFアルゴリズム" 京都大学数理解析研究所講究録941. 99-112 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 村尾: "多項式演算の並列高速アルゴリズムと並列DDFアルゴリズムへの応用" 京都大学数理解析研究所 短期共同研究集会、講究録. (印刷準備中).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 村尾: "Speeded Chinese remaindering" 日本数式処理学会第5回大会(「数式処理」に概要). 5. 56-57 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Fujise,T.and Murao,H.: "Parallel distinct degree factorization algorithm" Proc.1996 ISSAC (Ed.Lakshman.Y.N.,Ziirich). 18-25

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 村尾: "多項式の高速多点評価法とその並列処理について-高速プログラムの開発へ向けて-" 京都大学数理解析研究所 講究録986. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Murao,H.and Fujise,T.: "Modular algorithm for sparse multivoriate polynomial interpolation and its parallel implementation" Journal of Symbolic Computation. 21. 377-396 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 村尾,藤瀬: "並列処理の多項式計算への応用(解説論文)" 数式処理. Vol.5,No.1. 2-17 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Murao,H.and Fujise,T.: "Towards an efficient implementation of a fast algorithm for multipoint polynominal evaluation acid its parallel processing" Proc.PASCO'97. (発表予定). (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Fujise, T.and Murao, H.: "Parallel DDF algorithm. (in Japanese)" Kyoto University, RIMS Kokyuroku. No. 941, (Mar., 1996. Workshop held during Nov. 20-22,1995). 99-112

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Murao, H.: "Parallel fast algorithms for polynomial operations and their applications to parallel DDF algorithm. (in Japanese)" Kyoto University, RIMS Kokyuroku (in preparation), Short Term Cooperative Research "Researches on Algorithms for Computer Algebra" (Feb. 26-29,1996).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Murao, H.: "Speeded Chinese remaindering." JSSAC 5th Annual Symposium (Iwate Univ., May, 1996). Abstract (in Japanese) published in Journal of Japan Society for Symbolic and Algebraic Computation. Vol. 5, No. 1. 56-57 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Fujise, T.and Murao, H.: "Parallel distinct degree factorization algorithm." Proceedings of the 1996 International Symposium on symbolic and Algebraic Computation, (Ed. Lakshman Y.N., Zurich, Switzerland. Jul. 24-26,1996). 18-25

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Murao, H.: "Fast algorithm for multipoint evaluation of a polynomial and its parallelization. (in Japanese)" Kyoto University, RIMS kokyuroku. No. 986, (Workshop held during Nov. 18-21,1996), (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Murao, H.Fujise, T.: "Modular algorithm for sparse multivariate polynomial interpolation and its parallel implementation." Journal of Symbolic Computation. Vol. 21, No. 4-6. 377-396 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Murao, H., Fujise, T.: "Parallel processing in polynomial manipulations. (in Japanese)" Journal of Japan Society for Symbolic and Algebraic Computation. Vol. 5, No. 1. 2-17 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Murao, H., Fujise, T.: "Towards an efficient implementation of a fast algorithm for multipoint polynomial evaluation and its parallel processing." (to be presented at PASCO'97 : Second International Symposium on Parallel Symbolic Computation (Maui, Hawaii. Jul. 20-22,1997) and to be published in the proceedings).(1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Murao,H.and Fujise,T.: "Modular Algorithm for Sparse Multioariate Pdyurial Interpdation and its Parallel iuplemeutation" Journal of Symbdic Conputation. 21・4〜6. 377-396 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 村尾、藤瀬: "並列処理の多項式計算への応用(解説論文)" 日本数式処理学会学会誌「数式処理」. 5・1. 2-17 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Fujise,T.and Murao,H.: "Parallel Distinct Degree Factorization Algorithm" Roc.ISSAC'96. 18-25 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 村尾裕一: "Speeded Chinese Rewaindering (大会報告、要約)" 日本数式処理学会学会誌「数式処理」. 5・1. 56-57 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 村尾裕一: "多項式の高速多点評価法とその並列処理について" 京都大学数理解析研究所講究録No.986「数式処理における理論と応用の研究」. 224-233 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] H.Murao: "Modular Algorithm for Sparse Multiuavtate Polymnal Interpchation and it's Parallel Implerentation" Journal of Symbolic Computation. 印刷準備中 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 藤瀬哲朗: "並列DDFアルゴリズム" 京都大学数理解析研究所講究録. (出版準備中).

    • Related Report
      1995 Annual Research Report
  • [Publications] 村瀬裕一: "多項式因数分解へのスーパーコンピュータの応用" 第4回数式処理学会大会('95.6月5日〜7日@奈良女子大). (口頭発表).

    • Related Report
      1995 Annual Research Report
  • [Publications] 村尾裕一: "Risa/Asivの整数GCD計算の改良" ワークショップ「数式処理システムとその応用」(愛媛大学工学部,平成8年3月). (口頭発表).

    • Related Report
      1995 Annual Research Report
  • [Publications] 村尾裕一: "多項式演算の並列高速アルゴリズムと並列DDFアルゴリズムへの応用" 京都大学数理解析研究所 短期共同研究 「Researches Algorithms for Coputer Algebra」 集会,講究録用原稿. (準備中).

    • Related Report
      1995 Annual Research Report

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Published: 1995-04-01   Modified: 2016-04-21  

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