On Preemptive Scheduling of Unrelated Parallel Processors by Linear Programming

Complexity of preemptive minsum scheduling on unrelated parallel machines

We show that the problems of minimizing total completion time and of minimizing the number of late jobs on unrelated parallel machines, when preemption is allowed, are both NP-hard in the strong sense. The former result settles a long-standing open question. A special case of the unrelated machine model is the identical machine model with the restriction that a job can only be processed on a sp...

Flexible flowshop scheduling with equal number of unrelated parallel machines

This article addresses a multi-stage flowshop scheduling problem with equal number of unrelated parallel machines. The objective is to minimize the makespan for a given set of jobs in the system. This problem class is NP-hard in the strong sense, so a hybrid heuristic method for sequencing and then allocating operations of jobs to machines is developed. A number of test problems are randomly ge...

Scheduling MapReduce Jobs on Unrelated Processors

MapReduce framework is established as the standard approach for parallel processing of massive amounts of data. In this work, we extend the model of MapReduce scheduling on unrelated processors (Moseley et al., SPAA 2011) and deal with the practically important case of jobs with any number of Map and Reduce tasks. We present a polynomial-time (32 + ✏)-approximation algorithm for minimizing the ...

Analysis of a linear programming heuristic for scheduling unrelated parallel machines

Each of n jobs is to be processed without interruption on one of m unrelated parallel machines. The objective is to minimize the maximum completion time. A heuristic method is presented, the first stage of which uses linear programming to form a partial schedule leaving at most m 1 jobs unscheduled: the second stage schedules these m1 jobs using an enumerative method. For m 2 3, it is shown tha...

Preemptive Scheduling on Dedicated Processors: Applications of Fractional Graph Coloring