Lazy Self-Adjusting Bounded-Degree Networks for the Matching Model

Abstract

Self-adjusting networks (SANs) utilize novel optical switching technologies to support dynamic physical network topology reconfiguration. SANs rely on online algorithms to exploit this topological flexibility to reduce the cost of serving network traffic, leveraging locality in the demand. While prior work has shown the potential of SANs, the theoretical guarantees rely on a simplified cost model in which traversing and adjusting a single link has uniform cost.We initiate the study of online algorithms for SANs in a more realistic cost model, the Matching Model (MM), in which the network topology is given by the union of a constant number of bipartite matchings (realized by optical switches), and in which changing an entire matching incurs a fixed cost α. The cost of routing is given by the number of hops packets need to traverse.Our main result is a lazy topology adjustment method for designing efficient online SAN algorithms in the MM. We design and analyze online SAN algorithms for line, tree, and bounded degree networks in the MM, with cost ${\mathcal{O}}(\sqrt \alpha )$ times the cost of reference algorithms in the uniform cost model. We report on empirical results considering publicly available datacenter network traces, that verify the theoretical bounds.