AN IMPROVED PARALLEL ALGORITHM FOR A GEOMETRIC MATCHING PROBLEM WITH APPLICATION TO TRAPEZOID GRAPHS

Let B be a set of n b blue points and R a set of nrred points in the plane, where nb + nr = n. A blue point b and a red point r can be matched if r dominates b, that is, if x(b) ≤ x(r) and y( b) ≤ y(r). We consider the problem of finding a maximum cardinality matching between the points in B and the points in R. We give an adaptive parallel algorithm to solve this problem that runs in O(log2n) time using the CREW PRAM with O(n2+ε/log n) processors for some ε,0 < ε < 1.It follows that finding the minimum number of colors to color a trapezoid graph can be solved within these resource bounds