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A Polynomial Time Approximation Scheme for the Problem of Interconnecting Highways

Author

Listed:
  • Xiuzhen Cheng

    (University of Minnesota)

  • Joon-Mo Kim

    (University of Minnesota)

  • Bing Lu

    (University of Minnesota)

Abstract

The objective of the Interconnecting Highways problem is to construct roads of minimum total length to interconnect n given highways under the constraint that the roads can intersect each highway only at one point in a designated interval which is a line segment. We present a polynomial time approximation scheme for this problem by applying Arora's framework (Arora, 1998; also available from http:www.cs.princeton.edu/~arora). For every fixed c > 1 and given any n line segments in the plane, a randomized version of the scheme finds a $$\left( {1 + \frac{1}{c}} \right)$$ -approximation to the optimal cost in O(n O(c)log(n) time.

Suggested Citation

  • Xiuzhen Cheng & Joon-Mo Kim & Bing Lu, 2001. "A Polynomial Time Approximation Scheme for the Problem of Interconnecting Highways," Journal of Combinatorial Optimization, Springer, vol. 5(3), pages 327-343, September.
    • Handle: RePEc:spr:jcomop:v:5:y:2001:i:3:d:10.1023_a:1011497227406
    DOI: 10.1023/A:1011497227406
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