### Citations

2037 |
Network Flows: Theory, Algorithms, and Applications
- Ahuja, Magnanti, et al.
- 1993
(Show Context)
Citation Context ...commodity network, the max-flow is always equal to the min-cut. Theorem 1 In a single commodity network, the max-flow is equal to the min-cut. [due to Ford and Fulkerson, 1956] We refer the reader to =-=[AMO1993]-=- or to the original paper by Ford and Fulkerson [FF1956] for the proof. We will soon see that for the multicommodity case this result does not hold. 1sCS 6550 – Design and Analysis of Algorithms Profe... |

356 | Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
- Leighton, Rao
- 1999
(Show Context)
Citation Context ...is well-known that for a single commodity, the max-flow is equal to the min-cut; however, this does not generalize for multiple commodities. Here, we will discuss bounds developed by Leighton and Rao =-=[LR1999]-=- for a specific case which they call the uniform multicommodity flow problem. These bounds are quite useful in the sense that they have been used to design the first polynomial time approximation algo... |

325 | Faster and simpler algorithms for multicommodity flow and other fractional packing problems
- Garg, Konemann
- 1998
(Show Context)
Citation Context ... various conference proceedings. It is a seminal result in the study of multicommodity flow problems. Since its publication, other advances have been made. We briefly mention a few. Garg and Könemann =-=[GK1998]-=- find a polynomial time algorithm to obtain good approximations for the maximum concurrent multicommodity flow. The running time for their approach depends on the time to compute a single commodity mi... |

92 |
Multicommodity flows in planar graphs
- Okamura, Seymour
- 1981
(Show Context)
Citation Context ...lysis of Algorithms Professor: Dana Randall Lecture and notes by: Jessica L. Heier and Kael Stilp October 18, 2007 Figure 1: All demands and capacities are 1. The max-flow is 3/4 and the min-cut is 1.=-=[OS1981]-=- Lemma 2 In general multicommodity flow networks with k commodities, the max-flow is within a factor of k of the min-cut. Proof. Solve the max-flow problem separately for each commodity, using 1 k C(e... |

4 |
Sur le probléme des courbes gauches en topologie
- Ford, Fulkerson
- 1956
(Show Context)
Citation Context ...n-cut. Theorem 1 In a single commodity network, the max-flow is equal to the min-cut. [due to Ford and Fulkerson, 1956] We refer the reader to [AMO1993] or to the original paper by Ford and Fulkerson =-=[FF1956]-=- for the proof. We will soon see that for the multicommodity case this result does not hold. 1sCS 6550 – Design and Analysis of Algorithms Professor: Dana Randall Lecture and notes by: Jessica L. Heie... |

1 |
Garima Gupta(2005). “Heuristic improvements for computing maximum multicommodity flow and minimum multicut
- Batra, Garg
(Show Context)
Citation Context ... the running time of this algorithm for sparse graphs or instances with k > m/n, where k is the number of commodities, m is the number of edges, and n is the number of vertices. Finally, Batra, et al =-=[BGG2005]-=- study the maximum multicommodity flow problem, in which the objective is to maximize the total flow (as opposed to the concurrent flow that we have previously considered). They improve upon the runni... |