Space-Efficient Plane-Sweep Algorithms

We introduce space-efficient plane-sweep algorithms for basic planar geometric problems. It is assumed that the input is in a read-only array of n items and that the available workspace is Θ(s) bits, where lgn ≤ s ≤ n · lg n. In particular, we give an almost-optimal algorithm for finding the closest pair among a set of n points that runs in O(n/s+n·lg s) time. We give a simple algorithm to enumerate the intersections of n line segments that runs in O((n/s) · lg s+ k) time, where k is the number of reported intersections. When the segments are axis-parallel, we give an O(n/s + n · lg s)-time algorithm for counting the intersections, and an algorithm for enumerating the intersections whose running time is O((n/s) · lg s · lg lg s+n · lg s+k). We also present space-efficient algorithms to calculate the measure of axis-parallel rectangles.