An <i>O</i>(<i>n</i>) Time Algorithm for Scheduling UET-UCT of Bipartite Digraphs of Depth One on Two Processors

Abstract

Given n unit execution time (UET) tasks whose precedence constraints form a directed acyclic graph, the arcs are associated with unit communication time (UCT) delays. The problem is to schedule the tasks on two identical processors in order to minimize the makespan. Several polynomial algorithms in the literature are proposed for special classes of digraphs, but the complexity of solving this problem in general case is still a challenging open question. We present in this paper an O(n) time algorithm to compute an optimal schedule for the class of bipartite digraphs of depth one.

Scheduling UET-UCT DAGs of Depth Two on Two Processors

“…𝐵 is the set of sources and 𝑊 is the set of sinks. We need the following two Lemmas which are proved in [12].…”

“…Such DAG will be denoted by 𝐺 = (𝐴 ∪ 𝐵 ∪ 𝐶, 𝐸) . This algorithm is an extension of the 𝑂(𝑛) time algorithm for the class of bipartite digraphs of depth one presented in [12]. .…”