Developing Algorithm Designs for Large Scale Combinatorial Optimization Problems

2014 Fiscal Year Final Research Report

• Project/Area Number: 23500014
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Fundamental theory of informatics
• Research Institution: Toyohashi University of Technology
• Principal Investigator: FUJITO TOSHIHIRO 豊橋技術科学大学, 工学(系)研究科(研究院), 教授 (00271073)
• Co-Investigator(Kenkyū-buntansha): FUJIWARA Hiroshi 信州大学, 工学部, 准教授 (80434893)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: アルゴリズム / 組合せ最適化問題 / 近似保証 / 競合比解析

Outline of Final Research Achievements

1. Some NP-hard optimization problems on graphs and networks are considered such as min cost tree cover, directed Steiner tree, and b-edge dominating set. A new algorithm is designed and an improved approximation guarantee is obtained for each of those problems considered.
2. The guarding game problem is to compute the minimum number of guards needed to protect a specified region from an intruder entering into the region. The problem is shown to be effectively approximable when an intruder is confined to moves on a tree.
3. The multislope ski-rental problem is an extension of the classical ski-rental problem, and we analyze both infimum and supremum of its best possible competitive ratio over arbitrary instances. It is shown that for the (k+1)-slope problem, the infimum is (k+1)k/((k+1)k-kk), implying that the competitive ratio can be no better than e/(e-1)≒1.58 no matter how many options the player may have. It is also shown that the supremum is 2.47 for k = 2 and 2.75 for k = 3.

Free Research Field

計算機科学