Online B-Matchings for Reconfigurable Datacenters: The Power of Randomization

This paper studies the problem of how to dynamically optimize the topology of a reconfigurable datacenter network in a demand-aware manner: by accounting for the current traffic pattern and providing direct connectivity between frequently communicating racks, the datacenter's bandwidth efficiency can be improved. The underlying algorithmic challenge can be described as an online maximum weight $b$-matching problem, a generalization of maximum weight matching where each node has at most $b \geq 1$ incident matching edges. Recently, Bienkowski et al.~presented an $O(b)$-competitive deterministic algorithm and showed that this is asymptotically optimal. This paper initiates the study of randomized algorithms, and we present a $O(\log b)$-competitive solution and show that this is asymptotically optimal. We complement our theoretical results with extensive trace-driven simulations, based on real-world datacenter workloads.