Cascading divide-and-conquer: a technique for designing parallel algorithms

Reviewer: Thomas Rainer Michael Fischer

The authors present new approaches to the design of parallel divide-and-conquer algorithms for problems in computational geometry. Their techniques apply whenever the merging step can be implemented by using only a restricted set of operations on sorted lists. A fundamental contribution of this paper is an optimal parallel construction of the fractional cascading data structure introduced by Chazelle and Guibas. Efficient parallel algorithms are proposed for a trapezoidal decomposition problem, planar point location, the segment intersection detection problem, a visibility problem, and others. All these algorithms run in O(log n) time with either a linear or a sublinear number of processors in the CREW PRAM model. The paper is carefully written; however, all algorithms proposed are described only informally.