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Restricted track assignment with applications

  • Majid Sarrafzadeh
  • D. T. Lee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 650)

Abstract

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.

Keywords

Circle Graph Basic Interval High Track Segment Tree Arbitrary Instance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Majid Sarrafzadeh
    • 1
  • D. T. Lee
    • 1
  1. 1.Department of Electrical Engineering and Computer ScienceNorthwestern UniversityEvanston

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