Implementations of the Goldberg-Tarjan
                    maximum flow algorithm

Nguyen, Q. C.; Venkateswaran, Venkat

doi:10.1090/dimacs/012/02

Cited by 12 publications

(7 citation statements)

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“…This is in contrast with the work of [2] and [23], where on some problem classes the FIFO implementation is faster. In particular, the FIFO implementation of Anderson and Setubal [2] takes 41.6 seconds on Washington-RLG-Wide problems with 65,538 nodes compared with 1,081.3 seconds for their HL implementation.…”

mentioning

confidence: 66%

“…We use this code as a "sanity check" for our implementation and to facilitate the comparison of our data to the data reported in [2]. (As observed in [23] and confirmed by our data, the global update frequency used in ASF is too low for dense graphs. )…”

Section: Implementations Evaluatedmentioning

confidence: 78%

“…Indirect comparison shows that H PRF is faster than the implementations of [23] on all common problem classes, including Genrmf-Wide, Genrmf-Long, Washington-LineModerate, and Acyclic-Dense. Next we present experimental data for the problem families we studied and make family-specific comments.…”

Section: Resultsmentioning

confidence: 99%

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On Implementing the Push—Relabel Method for the Maximum Flow Problem

1997

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We study efficient implementations of the push-relabel method for the maximum flow problem. The resulting codes are faster than the previous codes, and much faster on some problem families. The speedup is due to the combination of heuristics used in our implementations: we show that the highest-level selection strategy gives better results when combined with both global and gap relabeling heuristics. We also exhibit a family of problems for which the running time of all implementations we consider is quadratic. 1. Introduction. The maximum flow problem is a classical combinatorial problem that arises in a wide variety of applications. In this paper we study implementations of the push-relabel [15], [18] method for the problem. The basic methods for the maximum flow problem include the network simplex method of Dantzig [7], [8], the augmenting path method of Ford and Fulkerson [13], the blocking flow method of Dinitz [11], and the push-relabel method of Goldberg and Tarjan [15], [18]. (An earlier algorithm of Cherkassky [5] has many features of the pushrelabel method.) The best theoretical time bounds for the maximum flow problem, based on the latter method, are as follows. An algorithm of Goldberg and Tarjan [18] runs in O(nm log(n 2 /m)) time, an algorithm of King et al. [22] runs in O(nm + n 2+ε ) time for any constant ε > 0, algorithms of Cheriyan et al. [3] run in O(n 3 /log n) time and O(nm + (n log n) 2 ) time with high probability, and an algorithm of Ahuja et al. [1] runs in O(nm log(n/(m √ U ) + 2)) time.Prior to the push-relabel method, several studies have shown that Dinitz's algorithm [11] is in practice superior to other methods, including the network simplex method [7], [8], Ford-Fulkerson algorithm [12], [13], Karzanov's algorithm [21], and Tarjan's algorithm [24]. See, e.g., [19]. Several recent studies (e.g., [2], [9], [10], and [23]) show that the push-relabel method is superior to Dinitz's method in practice.In this paper we study implementations of the push-relabel method. We evaluate several operation orderings and distance update heuristics. Unlike previous implementa-

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confidence: 66%

Section: Implementations Evaluatedmentioning

confidence: 78%

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On Implementing the Push—Relabel Method for the Maximum Flow Problem

1997

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“…Computational performance of algorithms for closely related problems, the maximum flow problem, and the (global, e.g., over all s,t pairs) minimum cut problem has been studied extensively; see, e.g., [AS93,CG97,DM89,Gol87,NV93] for computational studies of the former problem and [CGK+97, RT97, Lev97, NOI94, PR90] for the latter. Both problems can be solved well in practice: most instances that fit in RAM of a modern computer can be solved in a few minutes.…”

Section: Introductionmentioning

confidence: 99%

Cut Tree Algorithms: An Experimental Study

Goldberg¹,

Tsioutsiouliklis

2001

Journal of Algorithms

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“…Some of the algorithms that came out of this research have been shown to have practical impact as well. In particular, the push-relabel method [ 11,16] is the best currently known way for solving the maximum flow problem [2,8,23]. This method extends to the minimum-cost flow problem using cost scaling [ 11,17].…”

Section: Introductionmentioning

confidence: 99%