ON THE OPTIMAL STOCHASTIC SCHEDULING OF OUT-FORESTS

This paper presents new results on the problem of scheduling jobs on K greater-than-or-equal-to 1 parallel processors to stochastically minimize the makespan. The jobs are subject to out-forest precedence constraints, i.e., each job has at most one immediate predecessor, and job running times are independent samples from a given exponential distribution. We define a class of uniform out-forests in which all subtrees are ordered by an embedding relation. We prove that an intuitive greedy policy is optimal for K = 2, and that if out-forests satisfy an additional, uniform root-embedding constraint, then the greedy policy is optimal for all K greater-than-or-equal-to 2.