An Optimal Algorithm for Finding the Minimum Cardinality Dominating Set on Permutation Graphs
A dominating set D of an undirected graph G is a set of vertices such that every vertex not in D is adjacent to at least one vertex in D. Given a undirected graph G, the minimal cardinality dominating set problem is to find a dominating set of G with minimum number of vertices. The minimal cardinality dominating set problem is NP-hard for general graphs. For permutation graphs, the best-known algorithm ran in O(n log log n) time, where n is the number of vertices. In this paper, we present an optimal O(n) algorithm.
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