Connecting the maximum number of grid nodes to the boundary with non-intersecting line segments

Abstract

We consider the problem of finding the maximum number of nodes in a grid (from a given set of such nodes) that can be connected to the boundary of the grid by means of non-intersecting line segments parallel to the grid axes. The work is motivated from the VLSI/WSI array processor technology, and in particular, the single-track switch model for configurable array processors ([4]). The problem has been investigated by Bruck and Roychowdhury, who described an algorithm to find the maximum number of compatible connections of n given nodes in the grid in O(n3) time and O(n2) space ([2]). In this paper, we present methods that take advantage of the dependency of similar configurations and enable us to resolve the problem in O(n2log n) time and O(n2) space; instrumental in our algorithm is the use of a new type of priority search trees which is of interest in its own right.