A synchronous parallel max-flow algorithm for real-world networks

Abstract

We study computing maximum flows for real-worldnetworks. In contrast to prior studies, our implementation is bulksynchronous. Our algorithm applies push and relabel operationson all active vertices in parallel, and maintains a preflow througha delayed flow update approach with handshakes between flowpushing and flow receiving.In our implementation the heuristics are no longer entangledwith the push and relabel operations as in prior implementations.We apply two heuristics well known for the sequential algorithm,that is, global relabel and gap relabel, to our parallel implementation.Experiments on networks constructed for computer visionimages show that our parallel implementation on the target 8-core machine is up to 8.6 times faster than the best sequentialimplementation.We aslo propose a new augmenting path based heuristic forsmall-world graphs. On large social networks with up to billionsof edges our implementation achieves close to 40 times parallelspeedup.