I/O-optimal computation of segment intersections

We investigate the I/O-complexity of computing the trapezoidal decomposition deened by a set of N line segments in the plane. We present a randomized algorithm which solves optimally this problem requiring O(N B log M=B N B + K B) expected I/O operations, where K is the number of pairwise intersections, M is the size of available internal memory and B is the size of the block transfer. The proposed algorithm requires an optimal expected number of internal operations. As a by-product, the algorithm also solves the segment intersections problem requiring the same number of I/Os and internal operations.