Reporting All Segment Intersections Using an Arbitrary Sized Work Space

摘要

This paper presents an efficient algorithm for reporting all intersections among n given segments in the plane using work space of arbitrarily given size. More exactly, given a parameter s which is between Ω(1) and O(n) specifying the size of work space, the algorithm reports all the segment intersections in roughly 0(n~2/s~(1/2) + K) time using O(s) words of O(log n) bits, where K is the total number of intersecting pairs. The time complexity can be improved to O((n~2/s)log s + K) when input segments have only some number of different slopes.