On the generalized channel definition problem

The generalized channel definition problem has been modeled as the following partition problem. Let RP be a boundary defined by a rectilinear polygon in E² and let H be a set of holes defined by disjoint rectilinear polygons inside RP. For IP=(RP,H), p(IP) is used to denote the length of the line segments that define RP plus the sum of the length of the line segments that define the holes in H. The authors consider the RP-RP problem in which RP is partitioned into rectangles by introducing a set of orthogonal line segments with least total length. Then m(IP) is used to denote the total length of the partitioning segments in an optimal solution to IP. The problem of finding m(IP) given IP is NP-hard. In this paper an O(n log n) approximation algorithm is presented for the RP-RP problem that generates solutions with length at most 2.5p(IP)+6m(IP), where n is the total number of segments in RP and H