A (2 + ε)-approximation for scheduling parallel jobs in platforms

Abstract

We consider the problem of Scheduling parallel Jobs in heterogeneous Platforms: We are given a set J = {1,..., n} of n jobs, where a job j ∈ J is described by a pair (pj,qj) of a processing time p j ∈ ℚ>0 and the number of processors required qj ∈ ℕ. We are also given a set B of N heterogeneous platforms P1,...,PN, where each Pi contains mi processors for i ∈ {1,..., N}. The objective is to find a schedule for the jobs in the platforms minimizing the makespan. Unless P = NP there is no approximation algorithm with absolute ratio strictly better than 2 for the problem. We give a (2 + ε)-approximation for the problem improving the previously best known approximation ratio. © 2013 Springer-Verlag.