UET scheduling with unit interprocessor communication delays
Discrete Applied Mathematics
Introduction to algorithms
New complexity results on scheduling with small communication delays
Discrete Applied Mathematics - Special volume: Aridam VI and VII, Rutcor, New Brunswick, NJ, USA (1991 and 1992)
The complexity of scheduling trees with communication delays
Journal of Algorithms
Scheduling UET-UCT series-parallel graphs on two processors
Theoretical Computer Science
Scheduling In and Out Forests in the Presence of Communication Delays
IEEE Transactions on Parallel and Distributed Systems
Scheduling series-parallel orders subject to 0/1-communication delays
Parallel Computing - Special issue on task scheduling problems for parallel and distributed systems
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Optimal scheduling on parallel machines for a new order class
Operations Research Letters
Optimal preemptive scheduling on a fixed number of identical parallel machines
Operations Research Letters
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The class of quasi-interval orders contains properly two rich families of precedence graphs: interval orders and a subclass of series-parallel orders. In this paper, we consider the problem of scheduling unitary task systems with zero-one communication delays in order to minimize the total elapsed time for the execution of all the tasks. This problem is known to be NP-complete on an unlimited number of processors even for interval orders. When the precedence constraints are given by a quasi-interval order G and the communication delays are locally identical (which includes the UET-UCT case), we show that an optimal static scheduling can be determined in O(n log n + e) time where n denotes the number of tasks and e denotes the number of the precedence constraints in the transitive closure of G. Some extensions are discussed for nonquasi-interval orders.