## An Efficient Implementation Of A Scaling Minimum-Cost Flow Algorithm (1992)

Venue: | Journal of Algorithms |

Citations: | 104 - 7 self |

### BibTeX

@ARTICLE{Goldberg92anefficient,

author = {Andrew V. Goldberg},

title = {An Efficient Implementation Of A Scaling Minimum-Cost Flow Algorithm},

journal = {Journal of Algorithms},

year = {1992},

volume = {22},

pages = {1--29}

}

### Years of Citing Articles

### OpenURL

### Abstract

. The scaling push-relabel method is an important theoretical development in the area of minimum-cost flow algorithms. We study practical implementations of this method. We are especially interested in heuristics which improve real-life performance of the method. Our implementation works very well over a wide range of problem classes. In our experiments, it was always competitive with the established codes, and usually outperformed these codes by a wide margin. Some heuristics we develop may apply to other network algorithms. Our experimental work on the minimum-cost flow problem motivated theoretical work on related problems. Supported in part by ONR Young Investigator Award N00014-91-J-1855, NSF Presidential Young Investigator Grant CCR-8858097 with matching funds from AT&T and DEC, Stanford University Office of Technology Licensing, and a grant form the Powell Foundation. 1 1. Introduction. Significant theoretical progress has been made recently in the area of minimum-cost flow ...

### Citations

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Citation Context ...e admissible graph GA = (V; EA ) is the graph induced by the admissible arcs. A flow f is optimal if and only if there exists a price function p such that no arc is admissible with respect to f and p =-=[12]-=-. For a constant ffls0, a pseudoflow f is said to be ffl-optimal with respect to a price function p if, for every residual arc a, we have c p (a)s\Gammaffl. A pseudoflow f is ffl-optimal if f is ffl-o... |

582 |
Network Flows
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Citation Context ...y Office of Technology Licensing, and a grant form the Powell Foundation. 0 1 1. Introduction. Significant theoretical progress has been made recently in the area of minimum-cost flow algorithms (see =-=[1, 18]-=-). Practical performance evaluation of some of these algorithms is just starting [23]. Detailed studies of somewhat older methods include investigations of network simplex [21], cost-scaling [8], and ... |

540 | A New Approach to the Maximum Flow Problem
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Citation Context ...ush-relabel method of Goldberg and Tarjan [15, 20]. This method combines and extends the ideas of cost-scaling of Rock [30] (see also [8]), the push-relabel maximum flow method of Goldberg and Tarjan =-=[14, 19]-=-, and the relaxation method of Bertsekas [4]. This new method looks promising for two reasons. First, the inner loop of the method is based on the push-relabel algorithm for the maximum flow problem, ... |

83 |
Algorithms for Network Programming
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Citation Context ...ated to the scaling shortest path algorithm [16], which has been motivated by our experimental work. We compare our implementation to the established and widely available network simplex codes NETFLO =-=[26]-=- and RNET [21], and to the relaxation code RELAX [5]. The comparison is done on eight problem families produced by three generators. The problems in different families have different characteristics, ... |

70 |
A Strongly Polynomial Minimum Cost Circulation Algorithm
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Citation Context ...g the number of times the algorithm examines an arc. The version of this heuristic that we use is a modification of the one used in [17]. The theoretical justification of this technique is as follows =-=[31]-=-, [20]: if the current flow is ffl-optimal and the absolute value of an arc cost exceeds 2nffl, the push-relabel method will not change the flow on this arc. Thus the arc does not need to be examined ... |

55 | Scaling Algorithms for the Shortest Path Problem
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Citation Context ... effective. Our current implementation succeeds in using two additional heuristics to update prices during the computation. These heuristics are closely related to the scaling shortest path algorithm =-=[16]-=-, which has been motivated by our experimental work. We compare our implementation to the established and widely available network simplex codes NETFLO [26] and RNET [21], and to the relaxation code R... |

51 |
Finding Minimum-Cost Circulations by Successive Approximation
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Citation Context ... [21], cost-scaling [8], and relaxation [5]. In this paper we continue our work [17] on implementing one of the recent methods, the successive approximation push-relabel method of Goldberg and Tarjan =-=[15, 20]-=-. This method combines and extends the ideas of cost-scaling of Rock [30] (see also [8]), the push-relabel maximum flow method of Goldberg and Tarjan [14, 19], and the relaxation method of Bertsekas [... |

48 |
Efficient graph algorithms for sequential and parallel computers
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Citation Context ... [21], cost-scaling [8], and relaxation [5]. In this paper we continue our work [17] on implementing one of the recent methods, the successive approximation push-relabel method of Goldberg and Tarjan =-=[15, 20]-=-. This method combines and extends the ideas of cost-scaling of Rock [30] (see also [8]), the push-relabel maximum flow method of Goldberg and Tarjan [14, 19], and the relaxation method of Bertsekas [... |

43 |
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Citation Context ... ffl GRID-SQUARE family, X = Y ; ffl GRID-WIDE family, Y = 16 and X increases; ffl GRID-LONG family, X = 16 and Y increases. NETGEN is a "classical" generator developed by Klingman, Napier, =-=and Stutz [27]-=-. We used a version of NETGEN (obtained from DIMACS and fixed by Bland et. al. [6]) to generate two example families, NETGEN-HI and NETGEN-LO. The families are identical except for maximum capacity va... |

39 | Network flow algorithms - Tardos, Tarjan - 1990 |

36 |
Computational results of an interior point algorithm for large scale linear programming
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Citation Context ...TO-16 family examples have density 16; ffl GOTO-I family examples have density b p nc. The GRIDGRAPH generator, written by Resende [29] and based on a generator proposed by Karmarkar and Remakrishnan =-=[25]-=-, produces networks that form rectangular grids with a source and a sink. This generator has five parameters: grid height X, grid width Y , maximum capacity, maximum cost, and a seed for the random nu... |

30 |
Relaxation methods for minimum cost ordinary and generalized network flow problems
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Citation Context ...l performance evaluation of some of these algorithms is just starting [23]. Detailed studies of somewhat older methods include investigations of network simplex [21], cost-scaling [8], and relaxation =-=[5]-=-. In this paper we continue our work [17] on implementing one of the recent methods, the successive approximation push-relabel method of Goldberg and Tarjan [15, 20]. This method combines and extends ... |

29 |
Implementing Goldberg's max-flow algorithm: A computational investigation, Zeitschrift ffir Operations Research 33
- Derigs, Meier
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(Show Context)
Citation Context ...irst, the inner loop of the method is based on the push-relabel algorithm for the maximum flow problem, which in that context has been shown superior to previous codes in several experimental studies =-=[2, 3, 9, 11, 22, 28]-=-. Second, the successive approximation technique used in the method requires fewer iterations of the inner loop compared to the closely related cost-scaling. Performance of the previous implementation... |

28 |
Distributed Asynchronous Relaxation Methods for Linear Network Flow Problems. Working Paper, Laboratory for Information and Decision Systems
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- 1986
(Show Context)
Citation Context ...]. This method combines and extends the ideas of cost-scaling of Rock [30] (see also [8]), the push-relabel maximum flow method of Goldberg and Tarjan [14, 19], and the relaxation method of Bertsekas =-=[4]-=-. This new method looks promising for two reasons. First, the inner loop of the method is based on the push-relabel algorithm for the maximum flow problem, which in that context has been shown superio... |

23 |
A new max-flow algorithm
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(Show Context)
Citation Context ...ush-relabel method of Goldberg and Tarjan [15, 20]. This method combines and extends the ideas of cost-scaling of Rock [30] (see also [8]), the push-relabel maximum flow method of Goldberg and Tarjan =-=[14, 19]-=-, and the relaxation method of Bertsekas [4]. This new method looks promising for two reasons. First, the inner loop of the method is based on the push-relabel algorithm for the maximum flow problem, ... |

22 |
Scaling Techniques for Minimal Cost Network Flows
- Röck
- 1980
(Show Context)
Citation Context ...rk [17] on implementing one of the recent methods, the successive approximation push-relabel method of Goldberg and Tarjan [15, 20]. This method combines and extends the ideas of cost-scaling of Rock =-=[30]-=- (see also [8]), the push-relabel maximum flow method of Goldberg and Tarjan [14, 19], and the relaxation method of Bertsekas [4]. This new method looks promising for two reasons. First, the inner loo... |

21 |
An Efficient Implementation of the Network Simplex Method
- Grigoriadis
(Show Context)
Citation Context ...nce, however, may result in a substantial difference in the generated examples. 9 We compare our code against three widely available codes: NETFLO of Kennington and Helgason [26], RNET of Grigoriadis =-=[21]-=-, and RELAX of Bertsekas and Tseng [5]. The version of RELAX we used was RELAXT, April 1990, All these codes are written in Fortran and compiled using SUN Fortran compiler with the optimization option... |

18 |
Implementations of the GoldbergTarjan Maximum Flow Algorithm, Algorithms for Network Flows and Matching, Edited by D
- NGUYEN, VENKATESWARAN
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(Show Context)
Citation Context ...irst, the inner loop of the method is based on the push-relabel algorithm for the maximum flow problem, which in that context has been shown superior to previous codes in several experimental studies =-=[2, 3, 9, 11, 22, 28]-=-. Second, the successive approximation technique used in the method requires fewer iterations of the inner loop compared to the closely related cost-scaling. Performance of the previous implementation... |

16 |
An efficient implementation of the network interiorpoint method
- Resense, Veiga
(Show Context)
Citation Context ...nsity as follows: 8 ffl GOTO-8 family examples have density 8; ffl GOTO-16 family examples have density 16; ffl GOTO-I family examples have density b p nc. The GRIDGRAPH generator, written by Resende =-=[29]-=- and based on a generator proposed by Karmarkar and Remakrishnan [25], produces networks that form rectangular grids with a source and a sink. This generator has five parameters: grid height X, grid w... |

14 |
On the Computational Behavior of a Polynomial-Time Network Flow Algorithm
- BLAND, JENSEN
- 1992
(Show Context)
Citation Context ...e [1, 18]). Practical performance evaluation of some of these algorithms is just starting [23]. Detailed studies of somewhat older methods include investigations of network simplex [21], cost-scaling =-=[8]-=-, and relaxation [5]. In this paper we continue our work [17] on implementing one of the recent methods, the successive approximation push-relabel method of Goldberg and Tarjan [15, 20]. This method c... |

6 |
On implementing scaling push-relabel algorithms for the minimumcost flow problem
- Goldberg, Kharitonov
- 1993
(Show Context)
Citation Context ...e algorithms is just starting [23]. Detailed studies of somewhat older methods include investigations of network simplex [21], cost-scaling [8], and relaxation [5]. In this paper we continue our work =-=[17]-=- on implementing one of the recent methods, the successive approximation push-relabel method of Goldberg and Tarjan [15, 20]. This method combines and extends the ideas of cost-scaling of Rock [30] (s... |

6 | A fast implementation of a path-following algorithm for maximizing a linear function over a network polytope - Joshi, Goldstein, et al. - 1993 |

3 |
A speculative contraction method for the minimum cost flows: toward a practical algorithm
- Fujishige, lwano, et al.
- 1993
(Show Context)
Citation Context ...eed to be examined until the optimal flow value computation. Arc fixing can be done after every execution of refine. In the dual context, arc fixing corresponds to edge contraction. Fujishige et. al. =-=[13]-=- propose contracting edges earlier than the theory suggests. We use this idea in the 7 primal context and call the resulting heuristic speculative arc fixing. This heuristic fixes all arcs with the ab... |

2 |
Goldberg's Algorithm for the Maximum Flow in Prespective: a Computational Study
- Anderson, Setubal
(Show Context)
Citation Context ...irst, the inner loop of the method is based on the push-relabel algorithm for the maximum flow problem, which in that context has been shown superior to previous codes in several experimental studies =-=[2, 3, 9, 11, 22, 28]-=-. Second, the successive approximation technique used in the method requires fewer iterations of the inner loop compared to the closely related cost-scaling. Performance of the previous implementation... |

2 |
An Empirical Study of Recent Min Cost Flow Algorithms. Extended Abstract accepted by the Dimacs Netflow Challenge Workshop; full paper in revision for the proceedings of the workshop
- Bland, Cheriyan, et al.
- 1991
(Show Context)
Citation Context ...ccessive approximation technique used in the method requires fewer iterations of the inner loop compared to the closely related cost-scaling. Performance of the previous implementations of the method =-=[7, 17]-=- is mixed: on some problem classes these implementations work well, while on other classes -- not so well. The implementation described in this paper works better then our previous code SPUR [17] on m... |