RESTRICTED TRACK ASSIGNMENT WITH APPLICATIONS

Abstract

Consider a set of intervals S = {I1, I2, …, In}, where Ii = (li, ri), li, and ri are real numbers, and li < ri. We study a restricted track assignment problem (RTAP): if an interval Ia contains another interval Ib, then Ia must be assigned to a higher track than Ib, 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 runs in O(n log n) 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.