Restricted track assignment with applications
Consider a set of intervals S=I1, I2, ..., I n , where I i = (l i , r i ), l i , and r i are real numbers, and l i < r i . We study a restricted track assignment problem (RTAP): if an interval I a contains another interval I b then I a must be assigned to a higher track than I b , and the goal is to minimize the number of tracks used. The problem RTAP is shown to be NP-hard. An approximation algorithm that produces a solution within twice of the optimal is also presented and the bound is shown to be tight. The algorithm, uses a segment tree as the basic structure, runs in O(nlogn) time and requires linear space. The proposed approximation algorithm is employed to solve the problem of finding a maximum-weighted independent set in a circle graph, and related problems.
KeywordsCircle Graph Basic Interval High Track Segment Tree Arbitrary Instance
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