Costly Circuits, Submodular Schedules and Approximate Carathéodory Theorems

Hybrid switching -- in which a high bandwidth circuit switch (optical or wireless) is used in conjunction with a low bandwidth packet switch -- is a promising alternative to interconnect servers in today's large scale data centers. Circuit switches offer a very high link rate, but incur a non-trivial reconfiguration delay which makes their scheduling challenging. In this paper, we demonstrate a lightweight, simple and nearly-optimal scheduling algorithm that trades-off reconfiguration costs with the benefits of reconfiguration that match the traffic demands. Seen alternatively, the algorithm provides a fast and approximate solution towards a constructive version of Caratheodory's Theorem for the Birkhoff polytope. The algorithm also has strong connections to submodular optimization, achieves a performance at least half that of the optimal schedule and strictly outperforms state of the art in a variety of traffic demand settings. These ideas naturally generalize: we see that indirect routing leads to exponential connectivity; this is another phenomenon of the power of multi-hop routing, distinct from the well-known load balancing effects.