Scheduling of pipelined operator graphs

Abstract

We investigate a class of scheduling problems that arise in the optimization of SQL queries for parallel machines (Chekuri et al. in PODS'95, pp. 255-265, 1995). In these problems, an undirected graph is used to represent communication and inter-operator parallelism. The goal is to minimize the global response time of the system. We provide a polynomial time approximation scheme for the special cases where the operator graph is a tree, thereby improving on a polynomial time 2.87-approximation algorithm by Chekuri et al. The approximation scheme is generalized to the case where the operator graph has treewidth bounded by a constant. We analyze instances with small response times for general operator graphs: Deciding whether a response time of four time units can be reached is easy, but deciding whether a response time of six time units can be reached is NP-hard. Finally, we prove that for general operator graphs the existence of a polynomial time approximation algorithm with worst case performance guarantee better than 4/3 would imply P = NP. © The Author(s) 2011.