Various Approaches to Computationally Hard Combinatorial Optimization Problems

2022 Fiscal Year Final Research Report

• Project/Area Number: 18K11183
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 60020:Mathematical informatics-related
• Research Institution: Tokyo Denki University
• Principal Investigator: Chen Zhi-Zhong 東京電機大学, 理工学部, 教授 (00242933)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Keywords: 組合せ最適化問題 / 近似アルゴリズム / randomizedアルゴリズム / 固定パラメータアルゴリズム / オンラインアルゴリズム / 発見的手法 / NP困難性

Outline of Final Research Achievements

We designed, analyzed, and implemented efficient algorithms for computationally hard combinatorial optimization problems. The concrete targeted problems include the following: the rSPR distance problem of rooted binary phylogenetic trees, the maximally balanced connected graph tripartition problem, the minimum leaf-removal center problem of rooted binary phylogenetic trees, the metric maximum triangle packing problem, the k-path partition problem of directed graphs, the minimum total completion-time problem of job scheduling with testing, and so on. For each of the problems, we succeeded in designing new algorithms that outperform the previous bests. For most of our designed problems, we not only rigorously analyzed their theoretical performance, but also implemented them into computer programs and compared their performance against the previous bests with both practical datasets and simulated ones.

Free Research Field

Combinatorial Optimization

Academic Significance and Societal Importance of the Research Achievements

対象とした組合せ最適化問題（「生物系統樹のrSPR距離問題」、「生物系統樹の最少葉数除去問題」、「メトリック最大三角形パッキン問題」、「グラフのkパス分割問題」、「テスト付きスケジューリングの最小合計処理時間問題」、など）それぞれについて、以前知られていた最良なアルゴリズムよりよい性能を達成する新しいアルゴリズムを設計できたので、当該分野の発展に貢献できたと言える。特に、一部の問題は実世界において重要な応用を持っているので、本研究で設計したアルゴリズムを実装して得たプログラムは実世界の現場で使われて社会に貢献する可能性を秘めている。