We show a deterministic constant-time parallel algorithm for finding an
almost maximum flow in multisource-multitarget networks with bounded degrees
and bounded edge capacities. As a consequence, we show that the value of the
maximum flow over the number of nodes is a testable parameter on these
networks.Comment: 8 page

Csóka, Endre

English

arXiv

oai:arXiv.org:1005.0513We show a deterministic constant-time local algorithm for constructing an
approximately maximum flow and minimum fractional cut in
multisource-multitarget networks with bounded degrees and bounded edge
capacities. Locality means that the decision we make about each edge only
depends on its constant radius neighborhood. We show two applications of the
algorithms: one is related to the Aldous-Lyons Conjecture, and the other is
about approximating the neighborhood distribution of graphs by bounded-size
graphs. The scope of our results can be extended to unimodular random graphs
and networks. As a corollary, we generalize the Maximum Flow Minimum Cut
Theorem to unimodular random flow networks

Maximum flow is approximable by deterministic constant-time algorithm in sparse networks

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