The input/output complexity of sorting and related problems
Communications of the ACM
Elements of information theory
Elements of information theory
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs
Journal of Computer and System Sciences
Relations Among Complexity Measures
Journal of the ACM (JACM)
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Compression using efficient multicasting
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Time-space trade-off lower bounds for randomized computation of decision problems
Journal of the ACM (JACM)
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Bounds on fundamental problems in parallel and distributed computation
Bounds on fundamental problems in parallel and distributed computation
Complexity classification of network information flow problems
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
An Approximate Max-Steiner-Tree-Packing Min-Steiner-Cut Theorem
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Deterministic network coding by matrix completion
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On characterization of entropy function via information inequalities
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Capacity results for the discrete memoryless network
IEEE Transactions on Information Theory
Zero-error network coding for acyclic networks
IEEE Transactions on Information Theory
Polynomial time algorithms for multicast network code construction
IEEE Transactions on Information Theory
Insufficiency of linear coding in network information flow
IEEE Transactions on Information Theory
On the capacity of multiple unicast sessions in undirected graphs
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
On optimal communication cost for gathering correlated data through wireless sensor networks
Proceedings of the 12th annual international conference on Mobile computing and networking
Foundations and Trends® in Networking
The serializability of network codes
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Monotonicity testing and shortest-path routing on the cube
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
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We consider information networks in the absence of interference and noise, and present an upper bound on the rate at which information can be transmitted using network coding. Our upper bound is based on combining properties of entropy with a strong information inequality derived from the structure of the network.The undirected k-pairs conjecture states that the information capacity of an undirected network supporting k point-to-point connections is achievable by multicommodity flows. Our techniques prove the conjecture for a non-trivial class of graphs, and also yield the first known proof of a gap between the sparsity of an undirected graph and its capacity. We believe that these techniques may be instrumental in resolving the conjecture completely. We demonstrate the importance of the undirected k-pairs conjecture by connecting it with a long-standing open question in Input/Output (I/O) complexity. We also show that proving the conjecture would provide the strongest known lower bound for computation in the oblivious cell-probe model and give a non-trivial lower bound for two-tape oblivious Turing machines.Finally, we conclude by considering the capacity of directed information networks. We construct a family of directed graphs whose capacity is much larger than the rate achievable using only multicommodity flows. The gap that we exhibit is linear in the number of vertices, edges, and commodities of the graph, which is asymptotically optimal.