Results 1 - 10 of 136

Approximate Max-Flow Min-(multi)cut Theorems and Their Applications

by Naveen Garg, Vijay V. Vazirani, Mihalis Yannakakis - SIAM Journal on Computing , 1993
"... Consider the multicommodity flow problem in which the object is to maximize the sum of commodities routed. We prove the following approximate max-flow min-multicut theorem: min multicut O(logk) max flow min multicut; where k is the number of commodities. Our proof is constructive; it enables us ..."
Abstract - Cited by 160 (3 self) - Add to MetaCart
for the latter problem. 1 Introduction Much of flow theory, and the theory of cuts in graphs, is built around a single theorem - the celebrated max-flow min-cut theorem of Ford and Fulkerson [FF], and Elias, Feinstein and Shannon [EFS]. The power of this theorem lies in that it relates two fundamental graph

Wireless Network Information Flow

by Amir Salman Avestimehr , 710
"... Abstract — We present an achievable rate for general deterministic relay networks, with broadcasting at the transmitters and interference at the receivers. In particular we show that if the optimizing distribution for the information-theoretic cut-set bound is a product distribution, then we have a ..."
Abstract - Cited by 55 (15 self) - Add to MetaCart
complete characterization of the achievable rates for such networks. For linear deterministic finite-field models discussed in a companion paper [3], this is indeed the case, and we have a generalization of the celebrated max-flow min-cut theorem for such a network. I.

Two-unicast is hard

by Sudeep Kamath , David N C Tse , Chih-Chun Wang - in 2014 IEEE International Symposium on Information Theory (ISIT
"... Abstract-Consider the k-unicast network coding problem over an acyclic wireline network: Given a rate vector k-tuple, determine whether the network of interest can support k unicast flows with those rates. It is well known that the one-unicast problem is easy and that it is solved by the celebrated ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
by the celebrated max-flow min-cut theorem. The hardness of k-unicast problems with small k has been an open problem. We show that the two-unicast problem is as hard as any kunicast problem for k ≥ 3. Our result suggests that the difficulty of a network coding instance is related more to the magnitude of the rates

Wireless Network Information Flow: A Deterministic Approach

by A. Salman Avestimehr, et al. , 2009
"... In contrast to wireline networks, not much is known about the flow of information over wireless networks. The main barrier is the complexity of the signal interaction in wireless channels in addition to the noise in the channel. A widely accepted model is the the additive Gaussian channel model, and ..."
Abstract - Cited by 296 (42 self) - Add to MetaCart
or more destinations (all interested in the same information) and an arbitrary number of relay nodes. This result is a natural generalization of the celebrated max-flow min-cut theorem for wireline networks. We then use the insights obtained from the analysis of the deterministic model to study

Network Flow Based Multi-way Partitioning with Area and Pin Constraints

by Huiqun Liu, D. F. Wong - Proc. of the ACM International Symposium on Physical Design , 1998
"... Network flow is an excellent approach to finding mincuts because of the celebrated max-flow min-cut theorem. However, for a long time, it was perceived as computationally expensive and deemed impractical for circuit partitioning. Only until recently, FBB [1,2] successfully applied network flow to tw ..."
Abstract - Cited by 4 (1 self) - Add to MetaCart
Network flow is an excellent approach to finding mincuts because of the celebrated max-flow min-cut theorem. However, for a long time, it was perceived as computationally expensive and deemed impractical for circuit partitioning. Only until recently, FBB [1,2] successfully applied network flow

Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms

by Tom Leighton, Satish Rao - J. ACM , 1999
"... In this paper, we establish max-flow min-cut theorems for several important classes of multicommodity flow problems. In particular, we show that for any n-node multicommodity flow problem with uniform demands, the max-flow for the problem is within an O(log n) factor of the upper bound implied by ..."
Abstract - Cited by 357 (6 self) - Add to MetaCart
In this paper, we establish max-flow min-cut theorems for several important classes of multicommodity flow problems. In particular, we show that for any n-node multicommodity flow problem with uniform demands, the max-flow for the problem is within an O(log n) factor of the upper bound implied

Wireless Network Information Flow: A Deterministic Approach

by unknown authors , 2009
"... In contrast to wireline networks, not much is known about the flow of information over wireless networks. The main barrier is the complexity of the signal interaction in wireless channels in addition to the noise in the channel. A widely accepted model is the the additive Gaussian channel model, and ..."
Abstract - Add to MetaCart
or more destinations (all interested in the same information) and an arbitrary number of relay nodes. This result is a natural generalization of the celebrated max-flow min-cut theorem for wireline networks. We then use the insights obtained from the analysis of the deterministic model to study

A combinatorial study of linear deterministic relay networks

by S. M. Sadegh Tabatabaei Yazdi, Serap A. Savari , 2009
"... In the last few years the so called linear deterministic model of relay channels has gained popularity as a means of studying the ow of information over wireless communication networks, and this approach generalizes the model of wireline networks which is standard in network optimization. There is r ..."
Abstract - Cited by 7 (2 self) - Add to MetaCart
. There is recent work extending the celebrated max-flow/min-cut theorem to the capacity of a unicast session over a linear deterministic relay network which is modeled by a layered directed graph. This result was first proved by a random coding scheme over large blocks of transmitted signals. We demonstrate

NETWORK FLOWS AND THE MAX-FLOW MIN-CUT THEOREM

by Al Staples-moore , 2009
"... The Max-Flow Min-Cut Theorem is an elementary theorem within the field of network flows, but it has some surprising implications in graph theory. We define network flows, prove the Max-Flow Min-Cut Theorem, and show that this theorem implies Menger’s and König’s Theorems. ..."
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The Max-Flow Min-Cut Theorem is an elementary theorem within the field of network flows, but it has some surprising implications in graph theory. We define network flows, prove the Max-Flow Min-Cut Theorem, and show that this theorem implies Menger’s and König’s Theorems.

The max-flow min-cut theorem for countable networks

by Ron Aharoni, Eli Berger, Agelos Georgakopoulos, Amitai Perlstein, Philipp Sprüssel , 2007
"... We prove a strong version of the the Max-Flow Min-Cut theorem for countable networks, namely that in every such network there exist a flow and a cut that are “orthogonal” to each other, in the sense that the flow saturates the cut and is zero on the reverse cut. If the network does not contain infin ..."
Abstract - Cited by 5 (1 self) - Add to MetaCart
We prove a strong version of the the Max-Flow Min-Cut theorem for countable networks, namely that in every such network there exist a flow and a cut that are “orthogonal” to each other, in the sense that the flow saturates the cut and is zero on the reverse cut. If the network does not contain
Results 1 - 10 of 136