Parity Balancing Path Flow Decomposition and Routing

We examine a new approach to finding efficient routing paths in large networks (e.g. inter-datacenter networks). Such networks carry many simultaneous data transmissions and efficient routing paths need to be found for each transmission. One way this problem can be solved is by first finding a multi-commodity flow solution for all source-sink pairs. This provides traffic flow information for each connection but does not specify specific routing paths to use. We consider the problem of decomposing these flow solutions into a small numbers of routing paths. The specific problem we consider is the following: Given a flow with source and sink nodes s and t, we wish to exactly represent the flow as the sum of a small number of path flows. In this work, we describe a novel approach to finding good flow decomposition solutions using parity balancing path flows. We present two new algorithms termed OddCover and JointOddCover that provide theoretical performance guarantees and are effective in practice. Our experimental results demonstrate that the proposed algorithms are competitive with the best heuristic approach.