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UET scheduling with unit interprocessor communication delays. (English) Zbl 0634.90031
We consider the problem of scheduling a partially ordered set of unit execution time tasks (UET) on \(m>1\) processors where there is a communication delay of unit time between any pair of distinct processors. We show that the problem of finding an optimal schedule is NP-hard. A greedy schedule is one where no processor remains idle if there is some task available which it could process. We establish that the length of an arbitrary greedy schedule, \(\omega^ c_ g\) satisfies \[ \omega^ c_ g\leq (3-\frac{2}{m})\omega^ c_{opt}-(1-\frac{1}{m}) \] where \(\omega^ c_{opt}\) is the length of the optimal schedule. We define a generalized list schedule (a type of greedy schedule) and discuss anomalous behaviour of such schedules with respect to speed-up. The relevance of these results to the implementation of parallel languages is discussed.

90B35 Deterministic scheduling theory in operations research
68Q25 Analysis of algorithms and problem complexity
65K05 Numerical mathematical programming methods
Full Text: DOI
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