A VLSI Solution to the Vertical Segment Visibility Problem

We present a parallel algorithm to solve the visibility problem among n vertical segments in a plane, which can be implemented on a VLSI chip arranged as a mesh of trees. Our algorithm determines all the pairs of segments that "see" each other in time O(log n); while the fastest sequential algorithm requires O(n log n). A lower bound to the area-time complexity of this problem of O(n2 log2 n) is also derived.