Counting and reporting red/blue segment intersections

Abstract

We simplify the red/blue segment intersection algorithm of Chazelle et al: Given sets of n disjoint red and n disjoint blue segments, we count red/blue intersections in O(n log n) time using O(n) space or report them in additional time proportional to their number. Our algorithm uses a plane sweep to presort the segments; then it operates on a list of slabs that efficiently stores a single level of a segment tree. With no dynamic memory allocation, low pointer overhead, and mostly sequential memory reference, our algorithm performs well even with inadequate physical memory.