• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

2015 Fiscal Year Annual Research Report

数理論理学からの計算限界解析

Planned Research

Project AreaA multifaceted approach toward understanding the limitations of computation
Project/Area Number 24106002
Research InstitutionKyoto University

Principal Investigator

牧野 和久  京都大学, 数理解析研究所, 准教授 (60294162)

Co-Investigator(Kenkyū-buntansha) 河村 彰星  東京大学, 大学院総合文化研究科, 講師 (20600117)
垣村 尚徳  東京大学, 大学院総合文化研究科, 講師 (30508180)
小林 佑輔  筑波大学, システム情報系, 准教授 (40581591)
ロスマン ベンジャミン  国立情報学研究所, 大学共同利用機関等の部局等, 特任研究員 (90599177)
Project Period (FY) 2012-06-28 – 2017-03-31
Keywords反マトロイド
Outline of Annual Research Achievements

本研究では,数理論理学的な解析手法を用い,P≠NP予想に代表される計算限界に関する重要な未解決問題の解決を試みる.具体的には,記述複雑度と証明複雑度という2つの数理論理学の視点を通して解明を目指す.また,計算限界解明のための標準的な手法である情報理論・符号理論 (A02班)に基づく手法や領域・回路計算量(A03班)からの解析技法,さらに,境界他分野 (統計力学(C01班),量子力学(C02班),学習理論(C03班))の手法を数理論理学のレンズを通して解釈し直し計算量解析を行う.これらの横断的な共同研究を通して,数理論理学的な計算量理論の新しい基礎理論の展開,および,数理論理学に由来する新しい解析手法の開発も目指す.さらには,上記の研究成果を逆に利用することで,数理論理学を用いた効率的なアルゴリズム
を開発する.
具体的に,本年度は,反マトロイドをホーン規則を用いて表現することで,関連する様々な計算量的な問題にこたえるとともに,それらを利用した教育システムの設計への応用を議論した.これらの成果により,人工知能学会研究会優秀賞を受賞している.また,ポジモジュラ関数の最適化問題に対してその計算量の上界と下界を明らかにした.特にこれまで未解決として残されていた,ポジモジュラ関数の最小化が指数時間必要であることをしました.これらの成果により,FIT2015 船井ベストペーパー賞を受賞している.これ以外にも,ランダムウオークの脱乱化,線形相補性問題に対する成果,あるいは,パリティーゲームのパラメータ化計算量解析,グラフの辺素パス問題や一般化ターミナルバックアップ問題に対する計算量的成果などが挙げられる.

Current Status of Research Progress
Current Status of Research Progress

1: Research has progressed more than it was originally planned.

Reason

反マトロイドやポジモジュラの成果により,人工知能学会研究会優秀賞,FIT2015 船井ベストペーパー賞を受賞していて,国内外で評価されている.

Strategy for Future Research Activity

後も数理論理学的な解析手法を用い,計算限界の解明を目指す.また,計算限界解明のための標準的な手法である情報理論・符号理論 (A02班)に基づく手法や領域・回路計算量(A03班)からの解析技法,さらに,境界他分野 (統計力学(C01班),量子力学(C02班),学習理論(C03班))の手法を数理論理学のレンズを通して解釈し直し計算量解析を行う.
特に,本領域研究の他班との共同研究を推進するため,合同の研究集会や打ち合わせを活発に行う.解析結果を得るため,またその逆に,解析結果の実振る舞いを検証するために大規模な計算機実験を行う.

  • Research Products

    (30 results)

All 2016 2015

All Journal Article (17 results) (of which Int'l Joint Research: 6 results,  Peer Reviewed: 17 results) Presentation (13 results) (of which Int'l Joint Research: 10 results,  Invited: 1 results)

  • [Journal Article] Trichotomy for integer linear systems based on their sign patterns2016

    • Author(s)
      Kimura Kei、Makino Kazuhisa
    • Journal Title

      Discrete Applied Mathematics

      Volume: 200 Pages: 67~78

    • DOI

      10.1016/j.dam.2015.07.004

    • Peer Reviewed
  • [Journal Article] Online minimization knapsack problem2016

    • Author(s)
      Han Xin、Makino Kazuhisa
    • Journal Title

      Theor. Comput. Sci.

      Volume: 609 Pages: 185~196

    • DOI

      10.1016/j.tcs.2015.09.021

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Exact and approximation algorithms for weighted matroid intersection2016

    • Author(s)
      Chen-Chung Huang, Naonori Kakimura, Naoyuki Kamiyama
    • Journal Title

      Annual ACM-SIAM Symposium on Discrete Algorithms

      Volume: 27 Pages: 430-444

    • DOI

      10.1137/1.9781611974331.ch32

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Improved max-flow min-cut algorithms in a circular disk failure model with application to a road network2016

    • Author(s)
      Kensuke Otsuki, Yusuke Kobayashi, Kazuo Murota
    • Journal Title

      European Journal of Operational Research

      Volume: 248 Pages: 396-403

    • DOI

      10.1016/j.ejor.2015.07.035

    • Peer Reviewed
  • [Journal Article] Deterministic random walks on finite graphs2015

    • Author(s)
      Shuji Kijima, Kentaro Koga, Kazuhisa Makino
    • Journal Title

      Random Structures and Algorithms

      Volume: 46 Pages: 739-761

    • DOI

      10.1002/rsa.20533

    • Peer Reviewed
  • [Journal Article] The linear complementarity problems with a few variables per constraint2015

    • Author(s)
      Hanna Sumita, Naonori Kakimura, Kazuhisa Makino
    • Journal Title

      Mathematics of Operations Research

      Volume: 40 Pages: 1015-1026

    • DOI

      10.1287/moor.2014.0708

    • Peer Reviewed
  • [Journal Article] On randomized fictitious play for approximating saddle points over convex sets2015

    • Author(s)
      Khaled M. Elbassioni, Kazuhisa Makino, Kurt Mehlhorn, Fahimeh Ramezani
    • Journal Title

      Algorithmica

      Volume: 73 Pages: 441-459

    • DOI

      10.1007/s00453-014-9902-8

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Parameterized algorithms for parity games2015

    • Author(s)
      Jakub Gajarsk´y, Michael Lampis, Kazuhisa Makino, Valia Mitsou, Sebastian Ordyniak
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 9235 Pages: 336-347

    • DOI

      10.1007/978-3-662-48054-0_28

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Parameterized complexity of sparse linear complementarity problems2015

    • Author(s)
      Hanna Sumita, Naonori Kakimura, Kazuhisa Makino
    • Journal Title

      LIPIcs

      Volume: 43 Pages: 355-364

    • DOI

      10.4230/LIPIcs.IPEC.2015.355

    • Peer Reviewed
  • [Journal Article] Proportional cost buyback problem with weight bounds2015

    • Author(s)
      Yasushi Kawase, Xin Han, Kazuhisa Makino
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 9486 Pages: 794-808

    • DOI

      10.1007/978-3-319-26626-8_59

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Fence patrolling by mobile agents with distinct speeds2015

    • Author(s)
      A. Kawamura,Y. Kobayashi
    • Journal Title

      Distributed Computing

      Volume: 28 Pages: 147-154

    • DOI

      10.1007/s00446-014-0226-3

    • Peer Reviewed
  • [Journal Article] Computational benefit of smoothness: Parameterized bit-complexity of numerical operators on analytic functions and Gevrey’s hierarchy2015

    • Author(s)
      A. Kawamura, N. M¨uller, C. R¨osnick, and M. Ziegler
    • Journal Title

      Journal of Complexity

      Volume: 31 Pages: 689-714

    • DOI

      10.1016/j.jco.2015.05.001

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Simple strategies versus optimal schedules in multi-agent patrolling2015

    • Author(s)
      A. Kawamura, M. Soejima
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 9079 Pages: 261-273

    • DOI

      10.1007/978-3-319-18173-8_19

    • Peer Reviewed
  • [Journal Article] Finding a path in group-labeled graphs with two labels forbidden2015

    • Author(s)
      Yasushi Kawase, Yusuke Kobayashi, Yutaro Yamaguchi
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 9134 Pages: 797-809

    • DOI

      10.1007/978-3-662-47672-7_65

    • Peer Reviewed
  • [Journal Article] The edge-disjoint paths problem in Eulerian graphs and 4-edge-connected graphs2015

    • Author(s)
      Ken-ichi Kawarabayashi, Yusuke Kobayashi
    • Journal Title

      Combinatorica

      Volume: 35 Pages: 477-495

    • DOI

      10.1007/s00493-014-2828-6

    • Peer Reviewed
  • [Journal Article] The generalized terminal backup problem2015

    • Author(s)
      Attila Bern´ath, Yusuke Kobayashi, Tatsuya Matsuoka
    • Journal Title

      SIAM Journal on Discrete Mathematics

      Volume: 29 Pages: 1764-1782

    • DOI

      10.1137/140972858

    • Peer Reviewed
  • [Journal Article] The complexity of minimizing the difference of two M#-convex set functions2015

    • Author(s)
      Yusuke Kobayashi
    • Journal Title

      Operations Research Letters

      Volume: 43 Pages: 573-574

    • DOI

      10.1016/j.orl.2015.08.011

    • Peer Reviewed
  • [Presentation] ネットワーク型交渉ゲームの安定化アルゴリ ズム2016

    • Author(s)
      伊藤建洋,垣村尚徳,神山直之,小林佑輔, 岡本吉央
    • Organizer
      アルゴリズム研究会
    • Place of Presentation
      電気通信大学
    • Year and Date
      2016-03-06 – 2016-03-06
  • [Presentation] 多項式時間測度とランダム性について2015

    • Author(s)
      河村彰星
    • Organizer
      電子 情報通信学会コンピュテーション研究会
    • Place of Presentation
      大阪大学
    • Year and Date
      2015-12-01 – 2015-12-01
  • [Presentation] 塀の警邏2015

    • Author(s)
      河村彰星
    • Organizer
      スケジューリングシンポジウム
    • Place of Presentation
      東京
    • Year and Date
      2015-09-26 – 2015-09-27
  • [Presentation] Towards computational complexity theory on advanced function spaces in analysis2015

    • Author(s)
      A. Kawamura, F. Steinberg, M. Ziegler
    • Organizer
      Continuity, Computability, Constructivity { From Logic to Algorithms
    • Place of Presentation
      Kochel am See
    • Year and Date
      2015-09-14 – 2015-09-18
    • Int'l Joint Research
  • [Presentation] Invitation to real complexity theory: Algorithmic foundations to reliable numerics with bit-costs2015

    • Author(s)
      A. Kawamura, M. Ziegler
    • Organizer
      The 18th Korea-Japan Joint Workshop on Algorithms and Computation
    • Place of Presentation
      Incheon
    • Year and Date
      2015-08-21 – 2015-08-22
    • Int'l Joint Research
  • [Presentation] Total dual integrality of the linear complementarity problem2015

    • Author(s)
      Hanna Sumita, Naonori Kakimura, Kazuhisa Makino
    • Organizer
      The 22nd Interna- tional Symposium on Mathematical Pro- gramming
    • Place of Presentation
      Pittsurgh
    • Year and Date
      2015-07-12 – 2015-07-17
    • Int'l Joint Research
  • [Presentation] On the image and length of polynomial-time computable curves2015

    • Author(s)
      T. Katayama, A. Kawamura
    • Organizer
      Twelfth International Conference on Computability and Complexity in Analysis
    • Place of Presentation
      tokyo
    • Year and Date
      2015-07-12 – 2015-07-15
    • Int'l Joint Research
  • [Presentation] Towards computational complexity theory on advanced function spaces in analysis2015

    • Author(s)
      A. Kawamura, F. Steinberg, M. Ziegler
    • Organizer
      Twelfth International Conference on Computability and Complexity in Analysis
    • Place of Presentation
      tokyo
    • Year and Date
      2015-07-12 – 2015-07-15
    • Int'l Joint Research
  • [Presentation] Computational complexity of real functions2015

    • Author(s)
      A. Kawamura
    • Organizer
      German-Japanese Workshop on The- ory and Practice of Real Computation
    • Place of Presentation
      Meiji University
    • Year and Date
      2015-07-12 – 2015-07-12
    • Int'l Joint Research
  • [Presentation] Weihrauch reducibility in polynomial-time computable analysis2015

    • Author(s)
      A. Kawamura
    • Organizer
      Sixteenth International Workshop on Logic and Com- putational Complexity
    • Place of Presentation
      Kyoto
    • Year and Date
      2015-07-04 – 2015-07-05
    • Int'l Joint Research / Invited
  • [Presentation] Total dual integrality of the linear complementarity problem2015

    • Author(s)
      Hanna Sumita, Naonori Kakimura, Kazuhisa Makino
    • Organizer
      The 9th Japanese- Hungarian Symposium on Discrete Mathe- matics and Its Applications
    • Place of Presentation
      Fukuoka
    • Year and Date
      2015-06-02 – 2015-06-05
    • Int'l Joint Research
  • [Presentation] Finding a shortest non-zero path in group-labeled graphs2015

    • Author(s)
      Yusuke Kobayashi and Sho Toyooka
    • Organizer
      The 9th Japanese- Hungarian Symposium on Discrete Mathe- matics and Its Applications
    • Place of Presentation
      Fukuoka
    • Year and Date
      2015-06-02 – 2015-06-05
    • Int'l Joint Research
  • [Presentation] Algorithmic aspects of covering supermodular functions under matroid constraints2015

    • Author(s)
      Krist´of B´erczi, Tam´as Kir´aly, and Yusuke Kobayashi
    • Organizer
      The 9th Japanese- Hungarian Symposium on Discrete Mathe- matics and Its Applications
    • Place of Presentation
      Fukuoka
    • Year and Date
      2015-06-02 – 2015-06-05
    • Int'l Joint Research

URL: 

Published: 2018-01-16   Modified: 2023-03-16  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi