## Experimental evaluation of parametric max-flow algorithms (2007)

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Venue: | In WEA ’07: Proceedings of the 6th Workshop on Experimental Algorithms |

Citations: | 6 - 1 self |

### BibTeX

@INPROCEEDINGS{Babenko07experimentalevaluation,

author = {Maxim Babenko and Jonathan Derryberry and Andrew Goldberg and Robert Tarjan and Yunhong Zhou},

title = {Experimental evaluation of parametric max-flow algorithms},

booktitle = {In WEA ’07: Proceedings of the 6th Workshop on Experimental Algorithms},

year = {2007},

pages = {256--269}

}

### OpenURL

### Abstract

Abstract. The parametric maximum flow problem is an extension of the classical maximum flow problem in which the capacities of certain arcs are not fixed but are functions of a single parameter. Gallo et al. [6] showed that certain versions of the push-relabel algorithm for ordinary maximum flow can be extended to the parametric problem while only increasing the worst-case time bound by a constant factor. Recently Zhang et al. [14,13] proposed a novel, simple balancing algorithm for the parametric problem on bipartite networks. They claimed good performance for their algorithm on networks arising from a real-world application. We describe the results of an experimental study comparing the performance of the balancing algorithm, the GGT algorithm, and a simplified version of the GGT algorithm, on networks related to those of the application of Zhang et al. as well as networks designed to be hard for the balancing algorithm. Our implementation of the balancing algorithm beats both versions of the GGT algorithm on networks related to the application, thus supporting the observations of Zhang et al. On the other hand, the GGT algorithm is more robust; it beats the balancing algorithm on some natural networks, and by asymptotically increasing amount on networks designed to be hard for the balancing algorithm. 1

### Citations

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(Show Context)
Citation Context ... n vertices, m arcs, and integral arc capacities bounded by U are O(nm log m/(n log n) n) [10] and O(min{n 2/3 ,m 1/2 }mlog(n 2 /m)log U) [7]. The former algorithm is based on the push-relabel method =-=[8]-=-. Gallo et al. [6] show ⋆ Part of this work was done while the author was visiting Microsoft Research – SVC. ⋆⋆ Also Department of Computer Science, Princeton University.show to modify certain version... |

157 | On Implementing Push-Relabel Method for the Maximum Flow Problem
- Cherkassky, Goldberg
- 1997
(Show Context)
Citation Context .... In combination with [7], this gives an O(min{n 2/3 ,m 1/2 }m log(n 2 /m)log U min{n,log(nU)}) bound for the parametric problem. In practice, certain implementations of the push-relabel method (e.g. =-=[4]-=-) have better overall performance than those of the algorithm of [7], which makes the GGT algorithm a promising choice for the parametric flow problem. Zhang et al. [14] recently introduced an algorit... |

126 |
A fast parametric maximum flow algorithm and applications
- Gallo, Grigoriadis, et al.
- 1989
(Show Context)
Citation Context .... The parametric maximum flow problem is an extension of the classical maximum flow problem in which the capacities of certain arcs are not fixed but are functions of a single parameter. Gallo et al. =-=[6]-=- showed that certain versions of the push-relabel algorithm for ordinary maximum flow can be extended to the parametric problem while only increasing the worst-case time bound by a constant factor. Re... |

119 | Beyond the Flow Decomposition Barrier - Goldberg, Rao - 1998 |

50 |
A faster deterministic maximum flow algorithm
- King, Rao, et al.
- 1994
(Show Context)
Citation Context ...1], and flow sharing [6]. The current best time bounds for the ordinary maximum flow problem on a network with n vertices, m arcs, and integral arc capacities bounded by U are O(nm log m/(n log n) n) =-=[10]-=- and O(min{n 2/3 ,m 1/2 }mlog(n 2 /m)log U) [7]. The former algorithm is based on the push-relabel method [8]. Gallo et al. [6] show ⋆ Part of this work was done while the author was visiting Microsof... |

41 | Tarjan, Improved algorithms for bipartite network flow
- Ahuja, Orlin, et al.
- 1994
(Show Context)
Citation Context ...the arcs incident to the sink. Intuitively, this variability can keep SB from needing to push flow over long distances to reach the balanced state. Using capacitiessdistributed uniformly at random on =-=[1, 1000]-=-, this intuition was confirmed as shown in Fig. 5 and Table 4, where such variability improves the performance of SB almost to that of GGT. Fig. 6 and Table 5 also show how the competitiveness of SB i... |

38 |
A selection problem of shared fixed costs and network flows
- Rhys
- 1970
(Show Context)
Citation Context ...on a single parameter and are monotonically increasing (decreasing) functions of the parameter. Applications of parametric maximum flow beyond those of ordinary maximum flow include product selection =-=[3, 12]-=-, database record segmentation [5], repair kit selection [11], and flow sharing [6]. The current best time bounds for the ordinary maximum flow problem on a network with n vertices, m arcs, and integr... |

28 |
Mathematical Techniques for Efficient Record Segmentation in Large Shared Databases
- Eisner, Severance
- 1976
(Show Context)
Citation Context ...cally increasing (decreasing) functions of the parameter. Applications of parametric maximum flow beyond those of ordinary maximum flow include product selection [3, 12], database record segmentation =-=[5]-=-, repair kit selection [11], and flow sharing [6]. The current best time bounds for the ordinary maximum flow problem on a network with n vertices, m arcs, and integral arc capacities bounded by U are... |

24 |
On a selection problem
- Balinski
- 1970
(Show Context)
Citation Context ...on a single parameter and are monotonically increasing (decreasing) functions of the parameter. Applications of parametric maximum flow beyond those of ordinary maximum flow include product selection =-=[3, 12]-=-, database record segmentation [5], repair kit selection [11], and flow sharing [6]. The current best time bounds for the ordinary maximum flow problem on a network with n vertices, m arcs, and integr... |

8 |
Optimizing field repair kits based on job completion rate
- Mamer, Smith
- 1982
(Show Context)
Citation Context ...ng) functions of the parameter. Applications of parametric maximum flow beyond those of ordinary maximum flow include product selection [3, 12], database record segmentation [5], repair kit selection =-=[11]-=-, and flow sharing [6]. The current best time bounds for the ordinary maximum flow problem on a network with n vertices, m arcs, and integral arc capacities bounded by U are O(nm log m/(n log n) n) [1... |

7 | Experimental evaluation of a parametric flow algorithm
- Babenko, Goldberg
(Show Context)
Citation Context ...n problem [14]. This motivates experimental comparison between this algorithm and the GGT algorithm. Few experimental studies of the parametric flow problem have been published in the open literature =-=[2, 13, 14]-=-. Our codes are the same or better than the corresponding ones in these studies. The only other implementation we are aware of is based on an algorithm described in [9]. However, this implementation b... |

7 | A Simultaneous Parametric Maximum-Flow Algorithm for Finding the Complete Chain of Solutions
- Zhang, Ward, et al.
- 2004
(Show Context)
Citation Context ...ached. Theoretical analysis of the algorithm [13] assumes round-robin balancing (i.e., repeatedly iterating over a list of the members of V2), although our implementation uses a working set heuristic =-=[14]-=- that is different from simple round-robin balancing (See Section 3.2). 3.2 Implementation Details Next we describe a few details of our implementation of the star balancing algorithm. First, although... |

6 | The pseudoflow algorithm and the pseudoflow-based simplex for the maximum flow problem
- Hochbaum
- 1998
(Show Context)
Citation Context ... in the open literature [2, 13, 14]. Our codes are the same or better than the corresponding ones in these studies. The only other implementation we are aware of is based on an algorithm described in =-=[9]-=-. However, this implementation became available to us too late for comparison in the current paper. Our comparison between the GGT and star balancing algorithms involves several steps. First, one need... |

4 | Balancing applied to maximum network flow problems
- Tarjan, Ward, et al.
- 2006
(Show Context)
Citation Context ... versions of the push-relabel algorithm for ordinary maximum flow can be extended to the parametric problem while only increasing the worst-case time bound by a constant factor. Recently Zhang et al. =-=[14, 13]-=- proposed a novel, simple balancing algorithm for the parametric problem on bipartite networks. They claimed good performance for their algorithm on networks arising from a real-world application. We ... |