apply an optimal serial algorithm to those subproblems with no more than segments, and apply Goodrich's algorithm to the remainder.

We describe randomized parallel CREW PRAM algorithms for building trapezoidal diagrams of line segments in the plane. For general segments, we give an algorithm requiring optimal O(A + n logn) expected work and optimal O(logn) time, where A is the number of intersecting pairs of segments. If the segments form a simple chain, we give an algorithm requiring optimal O(n) expected work and O(logn log logn log n) expected time, and a simpler algorithm requiring O(n log n) expected work. The serial algorithm corresponding to the latter is the simplest known algorithm requiring O(n log n) expected operations. For a set of segments forming K chains, we give an algorithm requiring O(A+ n log n +K logn) expected work and O(logn log logn log n) expected time. The parallel time bounds require the assumption that enough processors are available, with processor allocations every logn steps.