Odd submodular functions, Dilworth functions and discrete convex functions
Mathematics of Operations Research
A combinatorial, strongly polynomial-time algorithm for minimizing submodular functions
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Journal of Combinatorial Theory Series B
Information Theory and Reliable Communication
Information Theory and Reliable Communication
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
The multicast capacity of deterministic relay networks with no interference
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
Combinatorial algorithms for wireless information flow
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Graphs, Networks and Algorithms
Graphs, Networks and Algorithms
An algorithmic framework for wireless information flow
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
IEEE Transactions on Information Theory
Cooperative diversity in wireless networks: Efficient protocols and outage behavior
IEEE Transactions on Information Theory
Cooperative Strategies and Capacity Theorems for Relay Networks
IEEE Transactions on Information Theory
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The linear deterministic model of relay channels is a generalization of the traditional directed network model which has become popular in the study of the flow of information over wireless communication networks. The max-flow/min-cut theorem of Ford and Fulkerson has recently been extended to this wireless relay model. This result was first proved by a random coding scheme over large blocks of transmitted signals. We demonstrate the same result with a deterministic, polynomial-time algorithm which takes as input a single transmitted signal instead of a long block of signals. The max-flow/min-cut theorem of Ford and Fulkerson is related to a number of famous results in combinatorics including Hall's marriage theorem. Hall's marriage theorem is a special case of a well-known result in matroid theory and in transversal theory named the Rado-Hall theorem. We show that the max-flow/min-cut theorem for linear deterministic relay networks is connected to (1) a two-dimensional transversal theorem for block matrices which is a new application of the Rado-Hall theorem and (2) a combinatorial result on sequences of block matrices which is obtained through results in submodular optimization.