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Design Methodology of Algorithms via Knowledge Base

Research Project

Project/Area Number 01550280
Research Category

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

Allocation TypeSingle-year Grants
Research Field 計算機工学
Research InstitutionTokyo University of Agriculture and Technology

Principal Investigator

NAKAMORI Mario  Tokyo University of Agriculture and Technology, Department of Computer Science, Professor, 工学部, 教授 (00111633)

Co-Investigator(Kenkyū-buntansha) UEMURA Shunsuke  Tokyo University of Agriculture and Technology, Department of Computer Science,, 工学部, 教授 (00203480)
Project Period (FY) 1989 – 1991
Project Status Completed (Fiscal Year 1991)
Budget Amount *help
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1991: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1990: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1989: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywordsalgorithm / data structure / combinatorial problems / algorithms on graphs / linear programming / computational complexity / education of algorithm / rotating dot matrices / グラフ処理システム / アルゴリズムベ-ス / グラフ処理言語 / アルゴリズム・ベ-ス
Research Abstract

Suppose an n by n dot matrix pattern (figure, letter, symbol, etc.) is represented as a sequence of n words in a computer memory, where each word consists of n bits. If a dot exists in the (i. j) -th position. i. e., i-th row and the j-th column of the matrix, then the j-th bit of the i-th word is 1 ; otherwise, the bit is 0 (Figure 1) (the leftmost bit of a word is the 0-th and the rightmost bit is the n-1 st). Then our problem is as follows : rotate counterclockwise by 90 the bits in these n words, i. e., move the j-th bit of the i-th word of the source to the i-th bit of the (n-l-j)-th word of the destination. We also consider problems of rotating the pattern by 180 and 270, reversing in vertical, horizontal, and diagonal direction.
Matrix representation of a pattern is often used in output devices such as printers and graphic displays. Therefore, this problem is a very priietical one. In this project we proposed an 0 (n log n) algorithm for this problem. Also, we discussed the analogy between this algorithm and the fast Fourier transform.
We investigated the algebraic structure of the group of rewriting rules of rotating algorithms and showed that the group is isomorphic to the group of rotating algorithms.

Report

(4 results)
  • 1991 Annual Research Report   Final Research Report Summary
  • 1990 Annual Research Report
  • 1989 Annual Research Report
  • Research Products

    (21 results)

All Other

All Publications (21 results)

  • [Publications] 中森 眞理雄: "変動式多重指数分割による数値表現方式" 電子情報通信学会論文誌. J72ーA. 1009-1011 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 中森 眞理雄: "2次元閉曲面内の複体の位相的性質を調べる算法とデ-タ構造" 電子情報通信学会論文誌. J72ーA. 1367-1370 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 中森 眞理雄: "ドットマトリクスの回転等に関する算法に対する書換規則のなす群について" 電子情報通信学会論文誌. J73ーA. 95-102 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 中森 眞理雄: "変動式多重分割による自然数表現法" 情報処理学会論文誌. 31. 939-942 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 中森 眞理雄: "情報工学系学科の教育における手回し計算器の活用" 情報処理学会論文誌. 31. 1547-1555 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Mario NAKAMORI: "A New Floating Point Representation of Numbers Based on Variably Multiple Exponential Cut" Transactions of the Institute of Electronics, Information and Communication Engineers. J72-A, No. 6. 1009-1011 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Mario NAKAMORI: "Algorithms and Data Structures of Detecting Topological Characteristics of Complexes in a Two Dimensional Closed Surface" Transactics of the Institute of Electronics, Information and Communication Engineers. J72-A, No. 8. 1367-1370 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Mario NAKAMORI: "On the Structure of the Group of Transforming Rules on Rotation Algorithms of a Dot Matrix" Transactions of the Institute of Electronics, Information and communication Engineers. J73-A, No. 1. 95-102 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Mario NAKAMORI: "A New Representation of Natural Numbers Based on Variably Multiple Decomposition" Transactions of the Information Processing Society of Japan. 31, No. 6. 939-942 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Mario NAKAMORI: "Hand Driven Calculator in Laboratory Exercises for BA Degree in Computer Science" Transactions of the Information Processing Society of Japan.31, No. 11. 1547-1555 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 中森 眞理雄: "アルゴリズム教育に必要な数学" 情報処理学会計算機教育シンポジウム報告集. 159-170 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 野瀬 隆: "手作業とプログラミングによる整列の演習" 情報処理学会 情報専門学科のコアカリキュラムシンポジウム報告集. 1-8 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 鶴崎 宏亀: "グリッドフリ-配線に対する分枝限定アルゴリズム" 情報処理学会第44回全国大会講演論文集. 1. 75-76 (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] 吉田 勝人: "最大流問題の近年の算法の実際的評価" 情報処理学会第44回全国大会講演論文集. 1. 91-92 (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] 中森 眞理雄: "アルゴリズムの線形計画法による基礎づけ" 情報処理学会第44回全国大会講演論文集. 1. 93-94 (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] 中森 眞理雄: "変動式多重分割による自然数・表現法" 情報処理学会論文誌. 31. 939-942 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 中森 眞理雄: "情報工学系学科の教育における手回し計算器の活用" 情報処理学会論文誌. 31. 1547-1555 (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] 中森眞理雄: "ドットマトリクスの回転等に関する算法に対する書換え規則のなす群について" 電子情報通信学会論文誌. J73-A. 95-102 (1990)

    • Related Report
      1989 Annual Research Report
  • [Publications] 中森眞理雄: "ドットマトリクスの回転等に関するアルゴリズムに対する変換群" 電子情報通信学会論文誌. J72-A. 1445-1448 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] 中森眞理雄: "2次元閉曲面内の複体の位相的性質を調べる算法とデ-タ構造" 電子情報通信学会論文誌. J72-A. 1367-1370 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] 中森眞理雄: "変動式多重指数分割による数値表現方式" 電子情報通信学会論文誌. J72-A. 1009-1011 (1989)

    • Related Report
      1989 Annual Research Report

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Published: 1989-04-01   Modified: 2016-04-21  

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