Theory of Parameterized Complexity for Local Search-Type Computation

2022 Fiscal Year Final Research Report

• Project/Area Number: 17H01698
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: Nagoya University
• Principal Investigator: Ono Hirotaka 名古屋大学, 情報学研究科, 教授 (00346826)
• Co-Investigator(Kenkyū-buntansha): 柳浦 睦憲 名古屋大学, 情報学研究科, 教授 (10263120)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: 組合せ最適化 / グラフ最適化 / 近傍構造 / パラメータ化計算量 / 近似アルゴリズム / 均衡計算 / 無秩序の代償 / 安定性の代償

Outline of Final Research Achievements

This research conducts parameterized analyses of local and neighborhood search, which are basic frameworks on which many meta-heuristic algorithms are based. Meta-heuristics are promising approaches for (NP-hard) combinatorial optimization problems. However, their theoretical analyses are not very successful, meaning that metaheuristic algorithms with good performance are based on the craftsmanship of algorithm designers. To fill the gap, we study local search-type algorithms from the viewpoint of parameterized analyses of neighborhood systems in the solution space. Many results were obtained over six years, including an extension of the research period by COVID-19. Many research results were obtained from the viewpoint of parameterized computational complexity for neighborhood search/local search, which was initially planned, and some of these results were extended to bounding equilibria such as Price of Anarchy (POA) and Price of Stability (PoA), in algorithmic game theory.

Free Research Field

理論計算機科学（Theoretical Computer Science）

Academic Significance and Societal Importance of the Research Achievements

組合せ最適化問題の重要性は社会のIT化・DX化に伴い，一層強く認識されるようになった．メタヒューリスティクスは多様な制約を持つ組合せ最適化問題を実践的に解く有望なアプローチであるが，理論的な裏付けに乏しいという問題がある．本研究はメタヒューリスティクスのエンジンとなる局所探索に関してパラメータ化計算量の観点から新たな「理論的な裏付け」を与えることを目指したものである．今回得られた結果は多岐にわたるが，その中でも局所探索の有用性を示すもの・困難性を示すもの（パラメータを固定したとしてもPLS完全等）がが，これらは高性能メタヒューリスティクスアルゴリズムを設計する上で有用な指針になると考えられる．