Time-optimal visibility-related algorithms on meshes with multiple broadcasting

The compaction step of integrated circuit design motivates the study of various visibility problems among vertical segments in the plane. One popular variant is referred to as the Vertical Segment Visibility problem (VSV, for short) and is stated as follows. Given a collection S of n disjoint vertical line segments in the plane, for every endpoint of a segment in S determine the first line segment, if any, interacted by a horizontal ray to the right (resp. left) originating from that endpoint. The contribution of this paper is to propose a time-optimal algorithm for the VSP problem on meshes with multiple broadcasting. The authors then use this algorithm to derive time-optimal solutions for two related problems. All the algorithms run in O(log n) time on a mesh with multiple broadcasting of size n × n. This is the first instance of time-optimal solutions for these problems known to us