Online and Offline Greedy Algorithms for Routing with Switching Costs

Abstract: Motivated by the use of high speed circuit switches in large scale data centers, we consider the problem of circuit switch scheduling. In this problem we are given demands between pairs of servers and the goal is to schedule at every time step a matching between the servers while maximizing the total satisfied demand over time. The crux of this scheduling problem is that once one shifts from one matching to a different one a fixed delay $\delta$ is incurred during which no data can be transmitted. For the offline version of the problem we present a $(1-\frac{1}{e}-\epsilon)$ approximation ratio (for any constant $\epsilon >0$). Since the natural linear programming relaxation for the problem has an unbounded integrality gap, we adopt a hybrid approach that combines the combinatorial greedy with randomized rounding of a different suitable linear program. For the online version of the problem we present a (bi-criteria) $ ((e-1)/(2e-1)-\epsilon)$-competitive ratio (for any constant $\epsilon >0$ ) that exceeds time by an additive factor of $O(\frac{\delta}{\epsilon})$. We note that no uni-criteria online algorithm is possible. Surprisingly, we obtain the result by reducing the online version to the offline one.