Abstract
A maximum weighted independent set of a permutation graph is a maximum subset of noncrossing chords in a matching diagram (i.e., a set Φ of chords with end-points on two horizontal lines). The problem of finding, among all noncrossing subsets of Φ 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 Θ(n log n) time and Θ(n) space algorithm, for solving the problem with n chords, is proposed. As an application, we solve the problem of finding, among all proper subsets with density at most k of an interval graph, one with maximum number of intervals.
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