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組み合わせ最適化における指数サイズ・多項式時間近傍の設計

Research Project

Project/Area Number 16092226
Research Category

Grant-in-Aid for Scientific Research on Priority Areas

Allocation TypeSingle-year Grants
Review Section Science and Engineering
Research InstitutionMeiji University

Principal Investigator

玉木 久夫  Meiji University, 理工学部, 教授 (20111354)

Co-Investigator(Kenkyū-buntansha) 井口 幸洋  明治大学, 理工学部, 准教授 (60201307)
Project Period (FY) 2004 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥11,400,000 (Direct Cost: ¥11,400,000)
Fiscal Year 2007: ¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2006: ¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2005: ¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2004: ¥2,100,000 (Direct Cost: ¥2,100,000)
Keywords組み合わせ最適化 / 巨大近傍 / グラフ分割 / 動的計画法 / 分枝分割 / 刻み分割 / 平面グラフ / グラフクラス / 局所探索 / 大規模近傍 / 近傍内最適化 / 木分割 / 局所探索法 / 多項式時間アルゴリズム / グラフ / ハードウェア化 / FPGA
Research Abstract

指数サイズ・多項式時間近傍の設計の基礎となるグラフ分割アルゴリズムの研究を続け、成果を得た。平面グラフの分枝幅決定および分枝分割アルゴリズムの実装法についての実験を行い、種々の工夫を行うことによって従来の実装法では扱うことのできなかった大きさのグラフについても幅決定と分割構成ができることを確認した。また、平面グラフに対する刻み幅決定アルゴリズムを平面グラフよりも広いクラスに拡張するための研究を行い、進展を見た。拡張の基礎として、細部が公刊されていなかった、平面グラフのアルゴリズムの正当性の証明のある部分について、わかりやすい別証を構成した。この証明とそれに基づいた刻み幅決定アルゴリズムは、次のような平面上の描画を持つグラフのクラスに拡張できる見通しがついている(この部分については発表準備中)。(1)どの辺も高々一本の辺と交差する。(2)交差する辺をすべて取り除いてできる描画の各面において、取り除かれた辺は高々一対である。(3)交差の総数は定数以内である。また、近傍解法のハードウェア化の基礎として、ルックアップ表と算術分解にもとづいた論理回路の構成法の応用で成果を挙げた。

Report

(4 results)
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (21 results)

All 2008 2007 2006 2005 2004

All Journal Article (18 results) (of which Peer Reviewed: 3 results) Presentation (3 results)

  • [Journal Article] Empirical study on branchwidth and branch decomposition of planar graphs2008

    • Author(s)
      Z. Bian, Q. Gu, M. Marzban, H. Tamaki, Y. Yoshitake
    • Journal Title

      Proc. ALENEXO8 1

      Pages: 152-165

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On designs of radix converte4s using arithmetic decompositions2007

    • Author(s)
      Y. Iguchi, T. Sasao, M. Matssuura
    • Journal Title

      Journal of Multiple-Valued Logic 13

      Pages: 503-520

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Design methods of radix converters using arithmetic decompositions2007

    • Author(s)
      Y. Iguchi, T. Sasao, M. Matsuura
    • Journal Title

      IEICE Trans. On Information and Systems E90-D

      Pages: 905-914

    • NAID

      110007522146

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A memory-based programmable logic device using look-up table cascade with synchronous static random access memories2006

    • Author(s)
      K.Nakamura, T.Sasao, M.Matsuura, K.Tanaka, K.Yoshizumi, H.Vakahara, Y.Iguchi
    • Journal Title

      Japanese Journal of Applied Physics Vol. 45, No. 4B

      Pages: 3295-3330

    • NAID

      120006813272

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On the probability of rendezvous in graphs2005

    • Author(s)
      M.Dietzfelbinger, H.Tamaki
    • Journal Title

      Random Structures and Algorithms 26(3)

      Pages: 266-288

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Optimal Branch-Decomposition of Planar Graphs in O(n^3) Time2005

    • Author(s)
      Q.-P.Gu, H.Tamaki
    • Journal Title

      Proc.32^<nd> International Conference on Automata, Languages, and Programming LNCS 3580

      Pages: 373-384

    • Related Report
      2005 Annual Research Report
  • [Journal Article] An FPGA design of AES encryption circuit with 128-bit key2005

    • Author(s)
      H.Qin, T.Sasao, Y.Iguchi
    • Journal Title

      Proc.of 16^<th> GLSVLSI

      Pages: 147-151

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Programmable logic device with an 8-stage cascade of 64K-bit asynchronous SRAMs2005

    • Author(s)
      K.Nakamura, T.Sasao, M.Matsuura, K.Tanaka, K.Yoshizumi, H.Qin, Y.Iguchi
    • Journal Title

      Proc.of Cool Chips VIII, IEEE Symposium on Low-Power and High-Speed Chips

    • NAID

      120006779758

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Hardware to compute Walsh coefficients2005

    • Author(s)
      Y.Iguchi, T.Sasao
    • Journal Title

      Proc.of 35th International Symposium on Multiple-Valued Logic

      Pages: 75-81

    • NAID

      10015557975

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On LUT cascade realizations of FIR filters2005

    • Author(s)
      T.Sasao, Y.Iguchi, T.Suzuki
    • Journal Title

      Proc.of 8th Euromicro Conference on Digital System Design : Architectures, Methods and Tools

      Pages: 467-474

    • NAID

      10015557961

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Matching Algorithms Are Fast in Sparse Random Graphs2004

    • Author(s)
      Holger Bast, Kurt Mehlhorn, Guido Schafer, Hisao Tamaki
    • Journal Title

      Proc.of the 21st Symposium on Theoretical Aspects of Computer Science (STACS04) LNCS2996

      Pages: 81-92

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On Geometric Structure of Global Roundings for Graphs and Range Spaces2004

    • Author(s)
      Tetsuo Asano, Naoki Katoh, Hisao Tamaki, Takeshi Tokuyama
    • Journal Title

      Proc.of the 9th Scandinavian Workshop on Algorithm Theory (SWAT04) LNCS3111

      Pages: 455-467

    • NAID

      120000861687

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Optimal branch-decomposition of planar graphs in $O(n^3)$time2004

    • Author(s)
      Qiangping Gu, Hisao Tamaki
    • Journal Title

      Simon Fraser University School of Computing Technical Report SFU-CMPT-TR2004-14

      Pages: 1-12

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On the probability of rendezvous in graphs2004

    • Author(s)
      Marin Dietzfelbinger, Hisao Tamaki
    • Journal Title

      Random Structures and Algorithms 26-3

      Pages: 266-288

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Area-time complexities of multi-valued decision diagrams2004

    • Author(s)
      S.Nagayama, T.Sasao, Y.Iguchi, M.Matsuura
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics Vol.e87-A, No.5

      Pages: 1020-1028

    • NAID

      110003212997

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A realization of multiple-output functions by a look-up table ring2004

    • Author(s)
      H.Qin, T.Sasao, M.Matsuura, K.Nakamura, S.Nagayama, Y.Iguchi
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics Vol.e87-A

      Pages: 3141-3150

    • NAID

      110003212851

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A method to evaluate logic functions in the presence of unknown inputs using LUT cascades2004

    • Author(s)
      Y.Iguchi, T.Sasao, M.Matsuura
    • Journal Title

      Proc.of the 34th International Symposium on Multiple-Valued Logic (ISMVL-2004)

      Pages: 302-308

    • Related Report
      2004 Annual Research Report
  • [Journal Article] {Realization of sequential circuits by look-up table ring2004

    • Author(s)
      T.Sasao, H.Nakahara, M.Matsuura, Y.Iguchi
    • Journal Title

      Proc.of The 2004 IEEE International Midwest Symposium on Circuits and Systems (MWSCAS 2004)

      Pages: 1517-1512

    • Related Report
      2004 Annual Research Report
  • [Presentation] 平面グラフの分枝分割アルゴリズムのより広いクラスへの拡張に向けて2008

    • Author(s)
      玉木久夫、吉武由実
    • Organizer
      情報処理学会アルゴリズム研究会
    • Place of Presentation
      広島
    • Year and Date
      2008-03-08
    • Related Report
      2007 Annual Research Report
  • [Presentation] グラフ彩色問題に対する列生成アプローチの高速化2008

    • Author(s)
      玉木久夫、平川宗則
    • Organizer
      情報処理学会アルゴリズム研究会
    • Place of Presentation
      広島
    • Year and Date
      2008-03-08
    • Related Report
      2007 Annual Research Report
  • [Presentation] テストパターンの静的圧縮における厳密解と貪欲解の比較2008

    • Author(s)
      八木沢圭、山崎浩二、細川利典、玉木久夫
    • Organizer
      電子情報通信学会ディペンダブルコンピューティング研究会
    • Place of Presentation
      東京
    • Year and Date
      2008-02-08
    • Related Report
      2007 Annual Research Report

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Published: 2004-04-01   Modified: 2018-03-28  

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