Working Set Theorems for Routing in Self-Adjusting Skip List Networks

This paper explores the design of dynamic network topologies which adjust to the workload they serve, in a demand-aware and online manner. Such self-adjusting networks (SANs) are enabled by emerging optical technologies, and can be found, e.g., in datacenters. SANs can be used to reduce routing costs by moving frequently communicating nodes topologically closer. However, such reconfigurations also come at a cost, introducing a need for online algorithms which strike an optimal balance between the benefits and costs of reconfigurations.This paper presents SANs which provide, for the first time, provable working set guarantees: the routing cost between node pairs is proportional to how recently these nodes communicated last time. Our SANs rely on a distributed implementation of skip lists (which serves as the topology) and provide additional interesting properties such as local routing. Our first contribution is SASL², which is a randomized and sequential SAN algorithm that achieves the working set property. Then we show how SASL² can be converted to a distributed algorithm that handles concurrent communication requests and maintains SASL²'s properties. Finally, we present deterministic SAN algorithms.