Parameterized Algorithms for Cluster-Graph Modification Problems

• Main Authors: Li-Hsuan Chen, 陳立軒
• Other Authors: Bang Ye Wu
• Format: Others
• Language: en_US
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/fzz4yp

博士 === 國立中正大學 === 資訊工程研究所 === 104 === \emph{Graph clustering} is an important issue in computer science. In general, we are given a graph with edges between similar objects, and the goal is to group the similar objects into clusters. A theoretical approach asks for editing a graph into disjoint cliques. Due to the wide applications, there are many formulated problem definitions. In this study, we show parameterized algorithms for some of the graph modification problems. A 2-clustering problem in general asks for a 2-partition such that the number of edges between the 2-partition and the non-edges in the same partition are as ``small'' as possible. As in many optimization problems, we developed several algorithms for the most frequently used cost functions: min-sum, min-max, and min-sum of squares. For the $p$-clusterings problems, in which the vertex set is split into $p$ clusters, we developed some ways to make use of the additional parameter $p$ to obtain better results with multiple parameters. We study the vertex deletion version and design an efficient algorithm with multiple parameters.