Machine Partitioning and Scheduling under Fault-Tolerance Constraints

Abstract

We consider the problem of computing fault-tolerant, redundant assignments of jobs to faulty parallel machines with objective to minimize the maximum machine load. In particular, we are given a set M of faulty parallel machines, each having an integer speed v i and failing independently with probability f i . We are also given a set of jobs to be processed on M , and a fault-tolerance constraint (1 \Gamma ffl), and we seek a redundant assignment OE that minimizes maximum machine load L1 (OE), subject to the constraint that, with probability no less than (1 \Gamma ffl), all the jobs have a copy on at least one active machine. We present a polynomial-time 4-approximation algorithm for identical speed machines and arbitrary job sizes, and a 2 l ln(jM j=ffl) ln(1=fmax) m -approximation algorithm for related speed machines and unit size jobs. Both algorithms are based on computing a collection fM 1 ; : : : ; M g of disjoint machine subsets such that, with probability no less than (1 \..