Heuristics and a Promising Branch-and-Reduce Algorithm for the Maximum Bounded-Degree-1 Set Problem

• Main Authors: Yi-Chi Liu, 劉奕志
• Other Authors: Bang-Ye Wu
• Format: Others
• Language: en_US
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/01896257938363790021

碩士 === 國立中正大學 === 資訊工程研究所 === 101 === Given a graph G = (V, E), a bounded-degree-1 set S is a vertex subset of G such that the maximum degree in G[S] is at most one. The Maximum Bounded-Degree-1 Set "Max 1-bds" problem is to find a bounded-degree-1 set S of maximum cardinality in G. It is an NP-hard problem and can not be approximated to a ratio greater than n^{e-1} in polynomial time for all e > 0 unless P = NP. In this thesis, we design and implement heuristic algorithms and branch-and-reduce algorithms based on variant strategies. Our the branch-and-reduce algorithms apply a very simple branching rule. From the experiment results, we observe that our heuristic algorithms find solutions with good qualities, and our branch-and-reduce algorithms are more efficient than the algorithm given by Moser et al. in most of test instances.