Hierarchical results on complexity classes and methods for evaluating logic synthesis systems

2021 Fiscal Year Final Research Report

• Project/Area Number: 16K00020
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: Hiroshima University
• Principal Investigator: Iwamoto Chuzo 広島大学, 先進理工系科学研究科(工), 教授 (60274495)
• Project Period (FY): 2016-04-01 – 2022-03-31
• Keywords: 計算複雑性

Outline of Final Research Achievements

It is strongly believed that in order to solve more difficult problems, we need more computational resources, such as space and time. Studies on hierarchies of complexity classes provide a theoretical evidence for such properties. In this research, we studied the computational complexity of several combinatorial problems, and proved that some of those problems are NP-hard. We also proposed placement algorithms which assign a set of minimum guards on a given polygon, and discussed the complexity of the placement problem.

Free Research Field

情報学基礎

Academic Significance and Societal Importance of the Research Achievements

理論計算機科学の分野で最も重要かつ有名な未解決問題はＰ≠ＮＰ予想の証明である．本予想は，ミレニアム懸賞問題としてアメリカのクレイ数学研究所によって100万ドルの懸賞金がかけられている７問題の一つである．本研究では，どのような問題がＮＰ完全になるのか，または多項式時間で解ける問題のクラスＰに属するのかを探究することで，予想の証明の手がかりを探った．その結果，十数個の組合せ問題がＮＰ完全になることを解明できた．