Parallel algorithm for direct domination on nonoverlapping rectangles

The author presents a parallel algorithm for a computational geometry problem which is motivated by the constraint graph used in compaction of VLSI circuits. Let R be a set of n nonoverlapping rectangles, whose sides are parallel to the x and y coordinate axes. The dominance graph on R is a directed graph with R as vertex set; for rectangles a and c in R, the dominance graph contains an edge (a, c) whenever c is immediately above a . The algorithm presented constructs the dominance graph on R . It has time complexity O(log² n), using n/log n processors, in the CREW-PRAM (parallel random access machine) model. The algorithm is optimal in complexity, since the problem of constructing the dominance graph has (sequential) time complexity Ω(n log n)