Deepening analysis methods for limits of computation through integration with optimization techniques

2016 Fiscal Year Final Research Report

• Project Area: A multifaceted approach toward understanding the limitations of computation
• Project/Area Number: 24106005
• Research Category: Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)
• Allocation Type: Single-year Grants
• Review Section: Science and Engineering
• Research Institution: Kwansei Gakuin University (2015-2016); Kyoto University (2012-2014)
• Principal Investigator: Katoh Naoki 関西学院大学, 理工学部, 教授 (40145826)
• Co-Investigator(Kenkyū-buntansha): 岩田 覚 東京大学, 大学院情報処理工学系研究科, 教授 (00263161) ; 岡本 吉央 電気通信大学, 大学院情報理工学研究科, 准教授 (00402660) ; 神山 直之 九州大学, マス・フォア・インダストリ研究所, 准教授 (10548134) ; 来嶋 秀治 九州大学, 大学院システム情報科学研究院, 准教授 (70452307)
• Project Period (FY): 2012-06-28 – 2017-03-31
• Keywords: 最適化理論 / 拡張定式化 / 疎性マトロイド / マトロイド・パリティ問題 / 計算限界分析 / #P困難 / 体積計算

Outline of Final Research Achievements

In this project, we obtained the following results.
1. On extended formulations that have been extensively studied recently, a compact representation is provided for sparsity matroids that play important roles both in theory and in practice. 2. The first polynomial-time algorithm is developed for the weighted linear matroid parity problem. 3. A novel reduction method (a hardness proof method) is developed among problems for which brute-force searches cannot be essentially surpassed, resulting in a new standard for the field of exponential-time computation. 4. A polynomial time deterministic approximation algorithm is presented to compute the volume of a 0-1 knapsack polytope which is known to be #P-hard.

Free Research Field

組合せ最適化