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On computing the capacity of relay networks in polynomial time

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2 Author(s)
Parvaresh, F. ; Hewlett-Packard Labs., Palo Alto, CA, USA ; Etkin, R.

The capacity or approximations to capacity of various single-source single-destination relay network models has been characterized in terms of the cut-set upper bound. In principle, a direct computation of this bound requires evaluating the cut capacity over exponentially many cuts. We show that the minimum cut capacity of a relay network under some special assumptions can be cast as a minimization of a submodular function, and as a result, can be computed efficiently. We use this result to show that the capacity, or an approximation to the capacity within a constant gap for the Gaussian, wireless erasure, and Avestimehr-Diggavi-Tse deterministic relay network models can be computed in polynomial time. We present some empirical results showing that computing constant-gap approximations to the capacity of Gaussian relay networks with around 300 nodes can be done in order of minutes.

Published in:

Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on

Date of Conference:

July 31 2011-Aug. 5 2011