A Polynomial Time Approximation Scheme for the Problem of Interconnecting Highways

Xiuzhen Cheng (), Joon-Mo Kim () and Bing Lu ()
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Xiuzhen Cheng: University of Minnesota
Joon-Mo Kim: University of Minnesota
Bing Lu: University of Minnesota

Journal of Combinatorial Optimization, 2001, vol. 5, issue 3, No 5, 327-343

Abstract: 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.

Keywords: interconnecting highways; polynomial time approximation scheme; minimum Steiner tree; patching; dynamic programming (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1011497227406

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