New Heuristics for the Minimum 3-Hitting Set Problem

• Main Authors: Kai-Lun Hsiao, 蕭凱倫
• Other Authors: Maw-Shang Chang
• Format: Others
• Language: en_US
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/53409143201541878157

碩士 === 國立中正大學 === 資訊工程研究所 === 101 === Let C = {C1,C2, . . . ,Cm} be a collection of subsets of a finite set S. A hitting set D is a subset of S such that for i = 1, 2, . . . ,m, |D ∩ Ci| ≥ 1. An instance (S,C) is an input of the Minimum d-Hitting Set problem if |Ci| ≤ d for 1 ≤ i ≤ m. The Minimum d-Hitting Set problem is NP-complete for d ≥ 2. In this thesis, we design three heuristic algorithms for the Minimum 3-Hitting Set (Min 3-hs) problem and implement them. We compare the solutions found by the heuristic algorithms. Moreover, we implement an exact algorithm based on the algorithm given by Wahlstr¨om [25] for the Min 3-hs problem. We take the solutions found by our heuristic algorithms as an initial upper bound in the exact algorithm. We design a data structure to speedup the exact algorithm for the Min 3-hs problem. We compare the running time of the exact algorithm for the Min 3-hs with the commercial optimization software, IBM ILOG CPLEX Optimizer.