New Heuristics for the Maximum Bounded-Degree-d Set Problem

• Main Authors: Hsing-Yi Lei, 雷興怡
• Other Authors: Maw-Shang Chang
• Format: Others
• Language: en_US
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/99839997550701177718

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-d set S is a vertex subset of G such that the maximum degree in G[S] is at most d. The MAXIMUM BOUNDED-DEGREE-d SET (MAX d-BDS) problem is to find a bounded degree-d set S of maximum cardinality in G. It is an NP-hard problem. The MAX 1-BDS problem 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 six heuristic algorithms combined with three reduction rules. From the experiment results, we observe that our heuristic algorithms find solutions with good qualities compared with the optimal solution found by IBM ILOG CPLEX Optimizer in DIMACS graphs and with the exact algorithm given by Moser et al. in graphs from real social networks.