Scheduling with sufficient loosely coupled processors
Journal of Parallel and Distributed Computing
Towards an architecture-independent analysis of parallel algorithms
SIAM Journal on Computing
Fault tolerance and scheduling issues in multiprocessor systems
Fault tolerance and scheduling issues in multiprocessor systems
An Almost-Linear Algorithm for Two-Processor Scheduling
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Well structured parallel programs are not easier to schedule
Well structured parallel programs are not easier to schedule
Scheduling on profiles of constant breadth
Scheduling on profiles of constant breadth
Worst Case Analysis of Lawler's Algorithm for Scheduling Trees with Communication Delays
IEEE Transactions on Parallel and Distributed Systems
Static scheduling algorithms for allocating directed task graphs to multiprocessors
ACM Computing Surveys (CSUR)
Parallel processor scheduling with delay constraints
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Optimal Task Scheduling of a Complete K-Ary Tree with Communication Delays
PPAM '01 Proceedings of the th International Conference on Parallel Processing and Applied Mathematics-Revised Papers
Scheduling Trees with Large Communication Delays on Two Identical Processors
Euro-Par '00 Proceedings from the 6th International Euro-Par Conference on Parallel Processing
Scheduling unitary task systems with zero-one communication delays for quasi-interval orders
Discrete Applied Mathematics
Scheduling interval orders with communication delays in parallel
Journal of Parallel and Distributed Computing
Scheduling trees with large communication delays on two identical processors
Journal of Scheduling
Computers and Operations Research
Task scheduling in distributed environment using genetic algorithm
AIC'09 Proceedings of the 9th WSEAS international conference on Applied informatics and communications
Geometric scheduling of 2-D UET-UCT uniform dependence loops
EUROMICRO-PDP'02 Proceedings of the 10th Euromicro conference on Parallel, distributed and network-based processing
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We consider the problem of scheduling tasks on multiprocessor architectures in the presence of communication delays. Given a set of dependent tasks, the scheduling problem is to allocate the tasks to processors such that the pre-specified precedence constraints among the tasks are obeyed and certain cost-measures (such as the computation time) are minimized. Several cases of the scheduling problem have been proven to be NP-complete [16], [10]. Nevertheless, there are polynomial time algorithms for interesting special cases of the general scheduling problem [12], [14], [10]. Most of these results, however, do not take into consideration the delays due to message passing among processors. In this paper we study the increase in time complexity of scheduling problems due to the introduction of communication delays. In particular, we address the open problem of scheduling Out-forests (In-forests) in a multiprocessor system of m identical processors when communication delays are considered. The corresponding problem of scheduling Out-forests (In-forests) without communication delays admits an elegant polynomial time solution as presented first by Hu in 1961 [12]; however, the problem in the presence of communication delays has remained unsolved. We present here first known polynomial time algorithms for the computation of the optimal schedule when the number of available processors is given and bounded and both computation and communication delays are assumed to take one unit of time. Furthermore, we present a linear-time algorithm for computing a near-optimal schedule for unit-delay out-forests. The schedule's length exceeds the optimum by no more than (m驴 2) time units, where m is the number of processors. Hence for two processors the computed schedule is strictly optimum.