Stochastic Load Balancing on Unrelated Machines

We consider the problem of makespan minimization on unrelated machines when job sizes are stochastic. The goal is to find a fixed assignment jobs machines, minimize expected value maximum load over all machines. For identical-machines special case size same across constant-factor approximation algorithm has long been known. Our main result first for general This achieved by (i) formulating lower bound using an exponential-size linear program that efficiently computable and (ii) rounding this while satisfying only specific subset constraints still suffice makespan. also two generalizations. budgeted problem, where subject scheduling target number (or reward) jobs. extend our obtain problem. second involves q-norm objectives, we want machine loads. Here give [Formula: see text]-approximation algorithm, which any q.