Maximum Independent Set of a Permutation Graph in k Tracks
نویسندگان
چکیده
A maximum weighted independent set of a permutation graph is a maximum subset of noncrossing chords in a matching diagram (i.e., a set of chords with end-points on two horizontal lines). The problem of nding, among all noncrossing subsets of with density at most k, one with maximum size is considered, where the density of a subset is the maximum number of chords crossing a vertical line and k is a given parameter. A (n logn) time and (n) space algorithm, for solving the problem with n chords, is proposed. As an application, we solve the problem of nding, among all proper subsets with density at most k of an interval graph, one with maximum number of intervals. 1. Introduction Consider two rows of distinct integer points in the xy-plane. The lower row is at y = b 1 and the upper row at y = b 2 , for some b 1 < b 2. A chord N i = (` i ; u i) is a
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