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Extending NP-Hardness via the development of computational Ramsey Theory

Research Project

Project/Area Number 15K00006
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Theory of informatics
Research InstitutionGunma University

Principal Investigator

Amano Kazuyuki  群馬大学, 大学院理工学府, 教授 (30282031)

Project Period (FY) 2015-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywords計算量理論 / 下界 / 離散数学 / P≠NP予想 / 論理回路 / 計算複雑性理論 / 多数決関数 / 論理関数 / 離散構造 / 計算量 / しきい値回路 / 計算複雑さ / 多項式しきい値表現
Outline of Final Research Achievements

The aim of this research is to investigate the complexity of various hard problems in combinatorics. We treat such a problem as a particular instance of NP problem, and try to develop the framework that can discuss the complexity of a particular instance instead of the usual worst case scenario. We apply an approach that combines the computer experiments and theoretical arguments, which is a unique feature of this research. As a result, we have succeeded to make large progress on various problems especially that appeared in the computational complexity theory. We published 7 papers and gave 14 presentations during this work.

Academic Significance and Societal Importance of the Research Achievements

我々が日頃直面する様々な計算問題がNP困難性を満たすことは良くあるが,近年の計算機やアルゴリズムの爆発的進展によって,このことは解きたい問題自身が計算不能であることをもはや意味しない.また,NP困難性は通常,ユーザーが直面する特定のインスタンスの複雑さについては手掛かりを与えない.本研究では,特に計算複雑性に関する様々な問題について進展を与えるとともに,その問題自身の難しさについても多くの知見を得ることができた.これは,上記の状況を打破し,個別インスタンスの困難性を議論可能な枠組み構築への端緒となる重要な成果であると考える.

Report

(5 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (18 results)

All 2019 2018 2017 2016

All Journal Article (5 results) (of which Peer Reviewed: 5 results,  Open Access: 2 results,  Acknowledgement Compliant: 1 results) Presentation (13 results) (of which Int'l Joint Research: 5 results,  Invited: 1 results)

  • [Journal Article] Depth Two (<i>n</i>-2)-Majority Circuits for <i>n</i>-Majority2018

    • Author(s)
      Kazuyuki Amano and Masafumi Yoshida
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

      Volume: E101.A Issue: 9 Pages: 1543-1545

    • DOI

      10.1587/transfun.E101.A.1543

    • NAID

      130007479524

    • ISSN
      0916-8508, 1745-1337
    • Year and Date
      2018-09-01
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Depth Two Majority Circuits for Majority and List Expanders2018

    • Author(s)
      Kazuyuki Amano
    • Journal Title

      LIPIcs (Leibniz International Proceedings in Informatics)

      Volume: 117

    • DOI

      10.4230/LIPICS.MFCS.2018.81

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Enumeration of Boolean functions of sensitivity three and inheritance of nondegeneracy2017

    • Author(s)
      Kazuyuki Amano
    • Journal Title

      Information Theory (ISIT), 2017 IEEE International Symposium on

      Volume: - Pages: 251-255

    • DOI

      10.1109/isit.2017.8006528

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the Number of p4-tilings by an n-Omino2017

    • Author(s)
      Kazuyuki Amano and Yoshinobu Haruyama
    • Journal Title

      Leibniz International Proceedings in Informatics (LIPIcs)

      Volume: 92

    • DOI

      10.4230/LIPIcs.ISAAC.2017.5

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On XOR Lemma for Polynomial Threshold Weight and Length2016

    • Author(s)
      Kazuyuki Amano
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 9618 Pages: 259-269

    • DOI

      10.1007/978-3-319-30000-9_20

    • ISBN
      9783319299990, 9783319300009
    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] 凹凸のあるピースにおけるアンチスライドパズルの解析2019

    • Author(s)
      木村 健斗, 天野 一幸
    • Organizer
      組み合わせゲーム・パズルプロジェクト(CGP) 第14回研究集会
    • Related Report
      2018 Annual Research Report
  • [Presentation] ポリオミノのisohedralタイリング数の解析2019

    • Author(s)
      佐藤 大河, 天野 一幸
    • Organizer
      情報処理学会 第171回アルゴリズム研究会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Away from Rivals2018

    • Author(s)
      Kazuyuki Amano and Shin-ichi Nakano
    • Organizer
      30th Canadian Conference on Computational Geometry (CCCG 2018)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] An Approximation Algorithm for the 2-Dispersion Problem2018

    • Author(s)
      Kazuyuki Amano, Shin-ichi Nakano
    • Organizer
      電子情報通信学会 コンピュテーション研究会
    • Related Report
      2018 Annual Research Report
  • [Presentation] アンチスライドパズルの解析2018

    • Author(s)
      木村健斗,天野一幸
    • Organizer
      日本OR学会SSOR2018
    • Related Report
      2018 Annual Research Report
  • [Presentation] 多数決関数を計算する2層の多数決回路について2018

    • Author(s)
      吉田 昌史,天野 一幸
    • Organizer
      2017年度 冬のLAシンポジウム
    • Related Report
      2017 Research-status Report
  • [Presentation] Enumeration of Boolean Functions of Sensitivity Three and Inheritance of Nondegeneracy2017

    • Author(s)
      Kazuyuki Amano
    • Organizer
      2017 IEEE International Symposium on Information Theory, ISIT 2017
    • Place of Presentation
      Aachen, Germany
    • Year and Date
      2017-06-25
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Enumeration of Boolean functions of sensitivity three and inheritance of nondegeneracy2017

    • Author(s)
      Kazuyuki Amano
    • Organizer
      IEEE International Symposium on Information Theory (ISIT 2017)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] On the Number of p4-tilings by an n-Omino2017

    • Author(s)
      Kazuyuki Amano and Yoshinobu Haruyama
    • Organizer
      28th International Symposium on Algorithms and Computation (ISAAC 2017)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Sensitivityが3の論理関数について2016

    • Author(s)
      天野 一幸
    • Organizer
      電子情報通信学会 コンピュテーション研究会
    • Place of Presentation
      広島大 (広島県東広島市)
    • Year and Date
      2016-12-21
    • Related Report
      2016 Research-status Report
  • [Presentation] 論理関数のPTF表現のXOR補題について2016

    • Author(s)
      天野 一幸,舘 将馬
    • Organizer
      2016年夏のLAシンポジウム
    • Place of Presentation
      かんぽの宿大和平群 (奈良県生駒郡)
    • Year and Date
      2016-07-19
    • Related Report
      2016 Research-status Report
  • [Presentation] 多項式しきい値表現のXOR補題と整数計画のテンソル積2016

    • Author(s)
      天野 一幸
    • Organizer
      日本OR学会 最適化の基盤とフロンティア研究部会
    • Place of Presentation
      東京理科大学(東京都新宿区)
    • Year and Date
      2016-04-23
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] On XOR Lemma for Polynomial Threshold Weight and Length2016

    • Author(s)
      Kazuyuki Amano
    • Organizer
      The 10th International Conference on Language and Automata Theory and Applications (LATA '16)
    • Place of Presentation
      プラハ(チェコ)
    • Year and Date
      2016-03-15
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research

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Published: 2015-04-16   Modified: 2020-03-30  

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