Scheduling in Switching Networks with Set-Up Delays

Abstract

We consider the (preemptive bipartite scheduling problem PBS) (Crescenzi et al., “On approximating a scheduling problem,” Journal of Combinatorial Optimization, vol. 5, pp. 287–297, 2001) arising in switching communication systems, where each input and output port can be involved in at most one communication at the same time. Given a set of communication tasks to be communicated from the transmitters to the receivers of such a system, we aim to find a schedule minimizing the overall transmission time. To achieve this, we allow the preemption of communication tasks. However, in practice preemption comes with a cost, d, and this renders the problem NP-hard (Gopal et al., “An optimal switching algorithm for multibeam satellite systems with variable bandwidth beams,” IEEE Trans. Commun., vol.30, pp. 2475–2481, 1982). In this paper, we present a $2 - \frac{1}{d+1}$ approximation algorithm, which is the first one for the PBS problem with approximation ratio strictly less than two. Furthermore, we propose a simple optimal polynomial time algorithm for a subclass of instances of the PBS problem.