General vs. Interval Mappings for Streaming Applications

This paper deals with the problem of mapping pipelined applications on heterogeneous platforms whose processors are subject to failures. We address a difficult bi-criteria problem, namely deciding which stages to replicate, and on which resources, in order to optimize the reliability of the schedule, while guaranteeing a minimal throughput. Previous work had addressed the complexity of interval mappings, where the application is partitioned into intervals of consecutive stages (which are then replicated and assigned to processors). In this paper we investigate general mappings, where stages may be partitioned without any constraint, thereby allowing a better usage of processors and communication network capabilities. The price to pay for general mappings is a dramatic increase in the problem complexity. We show that computing the period of a given general mapping is an NP-complete problem, and we provide polynomial bounds to determine a (conservative) approximated value. The bi-criteria mapping problem itself becomes NP-complete on homogeneous platforms, while it is polynomial with interval mappings. We design a set of efficient heuristics, which we compare with interval mapping strategies through extensive simulations.