Improved bounds for matroid partition and intersection algorithms
SIAM Journal on Computing
Combinatorial optimization
Combinatorial algorithms for wireless information flow
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A simple combinatorial algorithm for submodular function minimization
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A dual approximation approach to weighted matroid intersection
Operations Research Letters
A max-flow/min-cut algorithm for a class of wireless networks
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Combinatiorial algorithms for wireless information flow
ACM Transactions on Algorithms (TALG)
Bounded-contention coding for wireless networks in the high SNR regime
DISC'12 Proceedings of the 26th international conference on Distributed Computing
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We consider the wireless relay network model as introduced by Avestimehr, Diggavi and Tse [2] for approximating Gaussian relay channels and show that it is a special case of a more abstract flow model that we introduce in this paper. This flow model is based on linking systems, a combinatorial structure with a tight connection to matroids. A main advantage of this flow model is that properties and algorithms can easily be derived from existing theory on matroids and linking systems. In particular we show a max-flow min-cut theorem and submodularity of cuts. Furthermore, efficient algorithms for matroid intersection or for matroid partition can be used for finding a maximum flow and a minimum cut. Thus, this approach can profit from well-established matroid (intersection or partition) algorithms, leading to faster algorithms for large capacity networks. Another advantage of our approach is that it is easy to extend or adapt it to similar problems. In particular, the algorithm we present for finding maximum flows can easily be adapted to find a maximum flow with minimum costs when costs are introduced on the inputs and outputs of the relays.