Parallel algorithms for maximum matching in complements of interval graphsand related problems

Given a set of n intervals representing an interval graph, the problem of f inding a maximum matching between pairs of disjoint (nonintersecting) inter vals has been considered in the sequential model. In this paper we present parallel algorithms for computing maximum cardinality matchings among pairs of disjoint intervals in interval graphs in the EREW PRAM and hypercube mo dels. For the general case of the problem, our algorithms compute a maximum matching in O (log(3) n) time using O (nl log(2) n) processors on the EREW PRAM and using n processors on the hypercubes. For the case of proper inte rval graphs, our algorithm runs in O (log n) time using O (n) processors if the input intervals are not given already sorted and using O (n/log n) pro cessors otherwise, on the EREW PRAM. On n-processor hypercubes, our algorit hm for the proper interval case takes O (log n log log n) time for unsorted input and O (log n) time for sorted input. Our parallel results also lead to optimal sequential algorithms for computing maximum matchings among disj oint intervals. In addition, we present an improved parallel algorithm for maximum matching between overlapping intervals in proper interval graphs.