A Message-Optimal Distributed Graph Algorithm: Partial Precedence Constrained Scheduling

This paper presents a distributed algorithm for the partial precedence constrained scheduling problem. In the classical precedence constrained scheduling problem all the dependent tasks must be scheduled before the task itself can be scheduled. The partial precedence constrained scheduling problem is a generalized version of the original precedence constrained problem in the sense that the number of dependent tasks to be scheduled before the task itself can be scheduled is considered a variable. Using a directed graph to model the partial precedence constrained scheduling problem in which n nodes represent the tasks and e edges represent the precedence constraints, it is shown that the distributed algorithm requires O(e) messages and O(n) units of time and is optimal in communication complexity to within a constant factor.