PARALLEL ALGORITHMS FOR THE SEGMENT DRAGGING PROBLEM

Abstract

We address a geometric problem called the segment dragging. We have n "obstacles" in the plane and want to preprocess them so that, given a query vertical line segment s, intersecting no obstacles, the first obstacle hit by s when we drag s horizontally to the right can be found efficiently. We present an O(log n) time, O(n) processor parallel algorithm for preprocessing when the obstacles are points or nonintersecting line segments. After preprocessing, a query can be answered in O(log n) time using a single processor. Our model of parallel computation is the EREW PRAM.