  This paper initiates the study of online algorithms for the maximum weight
$b$-matching problem, a generalization of maximum weight matching where each
node has at most $b \geq 1$ adjacent matching edges. The problem is motivated
by emerging optical technologies which allow to enhance datacenter networks
with reconfigurable matchings, providing direct connectivity between frequently
communicating racks. These additional links may improve network performance, by
leveraging spatial and temporal structure in the workload. We show that the
underlying algorithmic problem features an intriguing connection to online
paging (a.k.a. caching), but introduces a novel challenge. Our main
contribution is an online algorithm which is $O(b)$-competitive; we also prove
that this is asymptotically optimal. We complement our theoretical results with
extensive trace-driven simulations, based on real-world datacenter workloads as
well as synthetic traffic traces.
