Extending NP-Hardness via the development of computational Ramsey Theory

2018 Fiscal Year Final Research Report

• Project/Area Number: 15K00006
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: Gunma 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
• Keywords: 計算量理論 / 下界 / 離散数学 / P≠NP予想 / 論理回路

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.

Free Research Field

計算量理論

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．