Approximation Algorithms for Submodular Optimization

2015 Fiscal Year Final Research Report

• Project/Area Number: 23300002
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Fundamental theory of informatics
• Research Institution: The University of Tokyo (2012-2015); Kyoto University (2011)
• Principal Investigator: Iwata Satoru 東京大学, 情報理工学(系)研究科, 教授 (00263161)
• Co-Investigator(Kenkyū-buntansha): TAKAZAWA Kenjiro 京都大学, 数理解析研究所, 助教 (10583859) ; TANIGAWA Shin-ichi 京都大学, 数理解析研究所, 助教 (30623540)
• Project Period (FY): 2011-04-01 – 2016-03-31
• Keywords: 離散最適化 / 劣モジュラ関数 / 近似アルゴリズム / NP困難 / ネットワーク / 離散凸性 / 巡回セールスマン問題 / 組合せ剛性理論

Outline of Final Research Achievements

Submodularity is known to be a common structure among various efficiently solvable discrete optimization problems. On the other hand, most discrete optimization problems that arise in practice are NP-hard, and researchers have designed efficient algorithms for finding approximately optimal solutions. Combining these two streams of research in discrete optimization, we have tried to develop a systematic approach to design approximation algorithms for a generic framework of submodular optimization. In particular, we have provided a 1/2-approximation algorithm for maximizing k-submodular functions. We have also designed an approximation algorithm for maximizing monotone k-submodular functions within the ratio of k/2(k-1).

Free Research Field

数理工学