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Summary: On-line Scheduling with Precedence
Constraints
Yossi Azar y
Tel-Aviv Univ.
Leah Epstein z
Tel-Aviv Univ.
Abstract
We consider the on-line problem of scheduling jobs with precedence con-
straints on m machines. We concentrate in two models, the model of uniformly
related machines and the model of restricted assignment. For the related ma-
chines model, we show a lower bound of
p
m) for the competitive ratio of
deterministic and randomized on-line algorithms, with or without preemptions
even for known running times. This matches the deterministic upper bound of
O(
p
m) given by Ja e. The lower bound should be contrasted with the known
bounds for jobs without precedence constraints. Speci cally, without prece-
dence constraints, if we allow preemptions then the competitive ratio becomes
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