A Polynomial Time Approximation Scheme for the problem of Interconnecting Highways

Abstract

The objective of the Interconnecting Highways problem is to construct roads of minimum total length to interconnect 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 in [2]. For every fixed c>1 and given any n line segments in the plane, a randomized version of the scheme finds a (1+1/c)-approximation to the optimal cost in O(n o(c)log n) time.