Excerpt from Randomized Parallel Algorithms for Trapezoidal Diagrams We give several algorithms for building trapezoidal diagrams of line segments in the plane. These algorithms reach or approach Optimality with respect to three parameters: the number n of segments, the number A of crossing pairs of segments, and the number K of chains. Here a chain is a sequence of segments such that a segment meets its successor in the sequence at an endpoint, and no endpoint is common to more than two segments. Specific values of these parameters correspond to problems in computational geometry that have been extensively studied. We consider these cases, as well as the general case, in the context of randomized parallel algorithms in the crew pram model. 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.