## How to Find a Minimum Spanning Tree in Practice (1991)

Venue: | results and New Trends in Computer Science, volume 555 of Lecture Notes in Computer Science |

Citations: | 4 - 0 self |

### BibTeX

@INPROCEEDINGS{Moret91howto,

author = {Bernard M. E. Moret and Henry D. Shapiro},

title = {How to Find a Minimum Spanning Tree in Practice},

booktitle = {results and New Trends in Computer Science, volume 555 of Lecture Notes in Computer Science},

year = {1991},

pages = {192--203},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

We address the question of theoretical vs. practical behavior of algorithms for the minimum spanning tree problem. We review the factors that influence the actual running time of an algorithm, from choice of language, machine, and compiler, through low-level implementation choices, to purely algorithmic issues. We discuss how to design a careful experimental comparison between various alternatives. Finally, we present some results from an ongoing study in which we are using: multiple languages, compilers, and machines; all the major variants of the comparison-based algorithms; and eight varieties of graphs with sizes of up to 130,000 vertices (in sparse graphs) or 750,000 edges (in dense graphs). 1 Introduction Finding spanning trees of minimum weight (minimum spanning trees or MSTs) is one of the best known graph problems; algorithms for this problem have a long history, for which see the article of Graham and Hell [6]. The best comparison-based algorithm to date, due to Gabow...

### Citations

594 |
Fibonacci heaps and their uses in improved network optimization algorithms
- Fredman, Tarjan
- 1987
(Show Context)
Citation Context ...log jV j) O(jV j) Prim d-heap O((jEj + djV j) log d jV j) O(jV j) Prim Fibonacci heap relaxed heap O(jEj + jV j log jV j) O(jV j) Cheriton and Tarjan [1] O(jEj log log jV j) O(jEj) Fredman and Tarjan =-=[3]-=- O(jEj \Delta fi(jEj; jV j)) O(jEj) Gabow et al. O(jEj \Delta log fi(jEj; jV j)) O(jEj) considering alternative designs for a problem such as the MST, where all algorithms are fast and thus where even... |

165 |
Trans-dichotomous algorithms for minimum spanning trees and shortest paths
- Fredman, Willard
- 1994
(Show Context)
Citation Context ...e fi(m; n) = minf i j log (i) nsm=n g (in particular, fi(jEj; jV j) = O(1) for any moderately dense graph, in which case the algorithm runs in optimal linear time); very recently, Fredman and Willard =-=[4]-=- have described a linear-time algorithm that uses address arithmetic and bit manipulations. Classical algorithms have slower asymptotic running times, but also tend to be simpler; for a review of thes... |

93 |
On the history of the minimum spanning tree problem
- Graham, Hell
- 1985
(Show Context)
Citation Context ...panning trees of minimum weight (minimum spanning trees or MSTs) is one of the best known graph problems; algorithms for this problem have a long history, for which see the article of Graham and Hell =-=[6]-=-. The best comparison-based algorithm to date, due to Gabow et al. [5], runs in almost linear time---its running time is O(jEj log fi(jEj; jV j)), where fi(m; n) = minf i j log (i) nsm=n g (in particu... |

78 |
Relaxed heaps: an alternative to Fibonacci heaps with applications to parallel computation
- Driscoll, Gabow, et al.
- 1988
(Show Context)
Citation Context ...cci and rank-relaxed heaps (we did not implement run-relaxed heaps, which can be seen to suffer from much larger overhead than rank-relaxed heaps) offer the largest number of choices. Driscoll et al. =-=[2]-=-, in their discussion of relaxed heaps, suggested storing in each node an array of child pointers of approximately log 2 jV j in length in order to reduce the large overhead associated with relaxed he... |

70 |
Finding minimum spanning trees
- Cheriton, Tarjan
- 1976
(Show Context)
Citation Context ...all O(jEj log jV j) O(jEj) Prim binary heap O(jEj log jV j) O(jV j) Prim d-heap O((jEj + djV j) log d jV j) O(jV j) Prim Fibonacci heap relaxed heap O(jEj + jV j log jV j) O(jV j) Cheriton and Tarjan =-=[1]-=- O(jEj log log jV j) O(jEj) Fredman and Tarjan [3] O(jEj \Delta fi(jEj; jV j)) O(jEj) Gabow et al. O(jEj \Delta log fi(jEj; jV j)) O(jEj) considering alternative designs for a problem such as the MST,... |

32 |
Pairing heaps: experiments and analysis
- Stasko, Vitter
- 1987
(Show Context)
Citation Context ...e heap by one. For more complex data structures, the choices become too numerous for an exhaustive comparison. In the case of pairing heaps, we relied on the experimental results of Stasko and Vitter =-=[10]-=- and implemented four variants: two-pass and multi-pass, each with or without the auxiliary structure discussed in their article. However, we only implemented these versions with dynamic insertion, be... |

22 | H.: An empirical analysis of algorithms for constructing a minimum spanning tree
- Moret, Shapiro
- 1991
(Show Context)
Citation Context ...these problems. We conclude by presenting some of the results that we have observed in a large, on-going experimental study of MST algorithms. We focus here on the first two topics; a companion paper =-=[9]-=- offers a more detailed analysis of our results, while a forthcoming technical report will present all of our data. 2 From Asymptotic Analysis to Actual Running Times 2.1 General considerations An alg... |

20 |
Priority queues with update and finding minimum spanning trees
- Johnson
- 1975
(Show Context)
Citation Context ...g of edges; Cheriton and Tarjan's algorithm; and Fredman and Tarjan's algorithm. In implementing Prim's algorithm, we used binary heaps, d-heaps (where we used d = max(2; jEj=jV j), following Johnson =-=[7]-=-, so as to balance the worst-case cost of the DELETEMIN and DECREASEKEY operations), splay trees, Fibonacci heaps, rank-relaxed heaps, and pairing heaps. The asymptotic running times (amortized or wor... |

13 |
Algorithms from P to NP
- Moret, Shapiro
- 1991
(Show Context)
Citation Context ...ibed a linear-time algorithm that uses address arithmetic and bit manipulations. Classical algorithms have slower asymptotic running times, but also tend to be simpler; for a review of these, consult =-=[8]-=-, Section 5.3. Table 1 summarizes the asymptotic behavior of the principal comparison-based algorithms. While the asymptotic behavior of the algorithms apparently indicates which algorithm is best, we... |

4 |
Efficient algorithms for minimum spanning trees on directed and undirected graphs
- Gabow, Galil, et al.
- 1986
(Show Context)
Citation Context ...e of the best known graph problems; algorithms for this problem have a long history, for which see the article of Graham and Hell [6]. The best comparison-based algorithm to date, due to Gabow et al. =-=[5]-=-, runs in almost linear time---its running time is O(jEj log fi(jEj; jV j)), where fi(m; n) = minf i j log (i) nsm=n g (in particular, fi(jEj; jV j) = O(1) for any moderately dense graph, in which cas... |