On Two-Processor Scheduling and Maximum Matching in Permutation Graphs

Abstract This paper gives an O(n log n) algorithm for computing the two-processor schedule for a set of n tasks, When the precedence constraints are specified by a transitively oriented permutation graph. This implies an O(n log n) algorithm for finding the maximum matching in a permutation graph, improving the O(n log2 n) algorithm of Bauernopper et al. (1995).