Designing Efficient Algorithms for Optimization Problems with Combinatorial Structures

2016 Fiscal Year Final Research Report

• Project/Area Number: 25730001
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Theory of informatics
• Research Institution: The University of Tokyo
• Principal Investigator: KAKIMURA Naonori 東京大学, 大学院総合文化研究科, 講師 (30508180)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: アルゴリズム / グラフマイナー理論 / 固定パラメータ・アルゴリズム / 線形相補性問題 / 疎性

Outline of Final Research Achievements

In this project, we designed efficient algorithms for continuous and discrete optimization problems using their combinatorial structures. For discrete optimization problems, we analyzed combinatorial structures such as the Erdos-Posa property for packing/covering integer programming problems. The analysis is based on structural graph theory. The structures we found are used to develop efficient fixed-parameter algorithms. For continuous optimization problems, we mainly focused on the linear complementarity problems. We discussed the integrality of the linear complementarity problems. We also proposed efficient algorithms for LCP exploiting the sparsity.

Free Research Field

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