Connecting the maximum number of grid nodes to the boundary with non-intersecting line segments
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 (). 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 (). 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.
KeywordsLine Segment Array Processor Connection Pattern Grid Boundary Dummy Node
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