  Reconfigurable optical topologies promise to improve the performance in
datacenters by dynamically optimizing the physical network in a demand-aware
manner. State-of-the-art optical technologies allow to establish and update
direct connectivity (in the form of edge-disjoint matchings) between
top-of-rack switches within microseconds or less. However, to fully exploit
temporal structure in the demand, such fine-grained reconfigurations also
require fast algorithms for optimizing the interconnecting matchings.
  Motivated by the desire to offload a maximum amount of demand to the
reconfigurable network, this paper initiates the study of fast algorithms to
find k disjoint heavy matchings in graphs. We present and analyze six
algorithms, based on iterative matchings, b-matching, edge coloring, and
node-rankings. We show that the problem is generally NP-hard and study the
achievable approximation ratios.
  An extensive empirical evaluation of our algorithms on both real-world and
synthetic traces (88 in total), including traces collected in Facebook
datacenters and in HPC clusters reveals that all our algorithms provide
high-quality matchings, and also very fast ones come within 95% or more of the
best solution. However, the running times differ significantly and what is the
best algorithm depends on k and the acceptable runtime-quality tradeoff.
