Excerpt from 0 (Logn) Parallel Time Intersection and Union Algorithms for a Set of Planar Disc Related problems, such as estimating the area of the union of many discs in the plane, were first posed by shamos, monte-carlo techniques for computing the volume of the union of n spheres in k dimensions were given in spirakis, They run in time O(nk) and are based on a method developed by karp, Luby, 83] for estimation of the failure probability of an n component system. Also, sharir, 83] shows how to construct the Voronoi diagram of a set of n circular bodies, in time O(nlog2n) About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.