A Study of the Spanning Star Forest Problem on BipartiteGraphs

• Main Authors: Yen-Yi Lin, 林晏禕
• Other Authors: Kun-Mao Chao
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/72147505010395127099

碩士 === 國立臺灣大學 === 資訊工程學研究所 === 96 === We study the spanning star forest problem (SSF) and its variation on bipartite graphs (BSSF). The relation between SSF and the dominating set problem (DOM), which has fruitful results in the literature, has been observed. The related optimization problems MSSF and MBSSF are of NP-Hard in general, and we hope to contribute to the issues by concentrating on theoretical aspects of approximation algorithms and combinatorial optimization. In this thesis we demonstrate a general framework for approximating MBSSF based on available results of the dominating set problem. We hope to solve this problem by the upper bounds of the domination number. Based on several available domination numbers with constraints, we devise a polynomial time algorithm which obtains a 0.67 approximation ratio for most instances. We also construct some combinatorial witness of such a dominating set efficiently. By extending the dominating set to corresponding spanning star forest, we claim to have efficient algorithms for MBSSF.