From Switch Scheduling to Datacenter Scheduling: Matching-Coordinated Greed is Good

BSTRACTPacket scheduling over a switch (interconnect) fabric is a wellstudied problem in distributed computing, with known near-optimal distributed bipartite matching based protocols. We initiate a theoretical study of distributed flow scheduling in datacenter networks. Building upon the observation that modern datacenter networks use Clos-like topologies similar to switch fabrics, we introduce a new k-sparse flow-matching (k=k-SFM) problem, a variant of the classical matching problem that captures the unique constraints imposed by flow scheduling in datacenter networks. In the k=k-SFM problem, we are given a weighted graph and an integer k. The goal is to assign a fractional flow value to each edge under the following three constraints: (1) for each edge, the assigned flow value is no greater than its input weight; (2) for each vertex, the sum of flow values assigned to edges incident to the vertex is at most the capacity of the vertex; and (3) for each vertex, at most k incident edges are assigned a non-zero flow value. The goal is to compute a feasible solution with the largest total fractional weight.