Scheduling series-parallel orders subject to 0/1-communication delays

Abstract We consider the problem P ∞|prec, c ij ∈{0,1}| κ of scheduling jobs with arbitrary processing times on sufficiently many parallel processors subject to series–parallel precedence constraints and 0/1-communication delays in order to minimize a regular performance measure κ . Such schedules without processor restrictions are used for generating approximate solutions for a restricted number of processors. For unit time communication delays we derive polynomial algorithms to construct optimal schedules when the performance measure κ is the makespan or the average weighted completion time. For n jobs and r precedence constraints, the run times of these algorithms are O (n+r) and O (n 3 ) , respectively. On the other hand, both problems are shown to be NP-hard in the same model for 0/1-communication delays.

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