PARALLEL ALGORITHMS FOR LONGEST INCREASING CHAINS IN THE PLANE AND RELATED PROBLEMS

Abstract

Given a set [Formula: see text] of n points in the plane such that each point in [Formula: see text] is asscociated with a nonnegative weight, we consider the problem of computing the single-source longest increasing chains among the points in [Formula: see text] This problem is a generalization of the plannar maximal layers problem. In this paper, we present a parallel algorithm that computes the single-source longest incresing chains in the plane in [Formula: see text] time using [Formula: see text] processors in the CREW PRAM computational model. We also solve a related problem of computing the all-pairs longest paths in an n-node weighted planar st-graph, in [Formula: see text] time using [Formula: see text] CREW PRAM processors. Both of our parallel algorithms are improvement over the previously best known results.