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.
Highlights
The problem of scheduling a set of tasks on a set of identical processors under a precedence relation has been studied for a long time
There are n tasks that have to be executed by m identical processors subject to precedence constraints and communication delays
In this paper we present an O (n) time algorithm to compute an optimal algorithm for the class of bipartite digraphs of depth one, that is the digraphs for which every vertex is either a source or a sink
Summary
The problem of scheduling a set of tasks on a set of identical processors under a precedence relation has been studied for a long time. A large amount of work in the literature studies this problem with a restriction on its structure: the time of execution of every task is one unit execution time (UET), the number of processors m is fixed, the communication delays are neglected, constant or one unit (UCT), or special classes of task graph are considered. The problem of two processors scheduling with communication delays is extensively studied [6] [7] It is proven in [8] that the problem P2 | pr= ec binary tree,= pi 1,= cij c | Cmax is NP-hard where c is a large integer, whereas this problem is polynomial when the task graph is a complete binary tree. In this paper we present an O (n) time algorithm to compute an optimal algorithm for the class of bipartite digraphs of depth one, that is the digraphs for which every vertex is either a source (without predecessors) or a sink (without successors)
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