## A Practical Minimum Spanning Tree Algorithm Using the Cycle Property (2003)

Venue: | IN 11TH EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA), NUMBER 2832 IN LNCS |

Citations: | 10 - 2 self |

### BibTeX

@INPROCEEDINGS{Katriel03apractical,

author = {Irit Katriel and Peter Sanders and Jesper Larsson Träff},

title = {A Practical Minimum Spanning Tree Algorithm Using the Cycle Property},

booktitle = {IN 11TH EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA), NUMBER 2832 IN LNCS},

year = {2003},

pages = {679--690},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present a simple new (randomized) algorithm for computing minimum spanning trees that is more than two times faster than the best previously known algorithms (for dense, "difficult" inputs). It is of conceptual interest that the algorithm uses the property that the heaviest edge in a cycle can be discarded. Previously this has only been exploited in asymptotically optimal algorithms that are considered impractical. An additional advantage is...

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Citation Context ...ler data structures. Interval maxima can be found in constant time by applying a standard technique that uses precomputed tables of total size O(n log n). The tables store prex minima and sux maxima [=-=4-=-]. We explain how to arrange these tables in such a way that F (u; v) can be found using two table lookups forsnding the JP-order, one exclusive-or operation, one operationsnding the most signicant no... |

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Citation Context ...e fastest on dense graphs. We took the pairing heap from their code and combined it with a faster, array based graph representation. 5 This implementation of JP consistently outperforms [12] and LEDA =-=[11]-=-. 3.1 Graph Representations One issue in comparing MST-algorithms for dense graphs is the underlying graph representation. The JP algorithm requires a representation that allows fast iteration over al... |

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Citation Context ...algorithm [10] is best for sparse graphs. Its running time is asymptotically dominated by the time for sorting the edges by weight. For dense graphs (m n), the Jarnk-Prim (JP) algorithm is better [5,=-= 15]-=-. Using Fibonacci heap priority queues, its execution time is O(n log n +m). Using pairing heaps [3] Moret and Shapiro [12] get quite favorable results in practice at the price of worse performance gu... |

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Citation Context ...ight. For dense graphs (m n), the Jarnk-Prim (JP) algorithm is better [5, 15]. Using Fibonacci heap priority queues, its execution time is O(n log n +m). Using pairing heaps [3] Moret and Shapiro [12=-=]-=- get quite favorable results in practice at the price of worse performance guarantees. On the theoretical side there is a randomized linear time algorithm [6] and an almost linear time deterministic a... |

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Citation Context ...orting the edges by weight. For dense graphs (m n), the Jarnk-Prim (JP) algorithm is better [5, 15]. Using Fibonacci heap priority queues, its execution time is O(n log n +m). Using pairing heaps [3]=-=-=- Moret and Shapiro [12] get quite favorable results in practice at the price of worse performance guarantees. On the theoretical side there is a randomized linear time algorithm [6] and an almost line... |

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Citation Context ...hat use further ideas from the asymptotically best theoretical algorithms. Besides a component forsltering edges, these algorithms have a component for reducing the number of nodes based on Boruvka's =-=[2, 13]-=- algorithm. Although this algorithm is conceptually simple, it seems unlikely that it is useful for internal memory algorithms on current machines. However node reduction has great potential for paral... |

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Citation Context ... of edges that are notsltered out is bounded from above by n=p. By setting p = p n=m both recursively solved MST instances can be made small. It remains tosnd an ecient way to implementsltering. King =-=[7-=-] suggests asltering scheme which requires an O n log m+n n preprocessing stage, after which thesltering can be done with O(1) time per edge (for a total of O(m)). The preprocessing stage runs Boruvk... |

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Citation Context ...full branching tree; that is, all the leaves of B are at the same level and each internal node has at least two sons. (3) B has at most 2n nodes. It is then possible to apply to B Komlos's algorithm [=-=9-=-] for maximum edge weight queries on a full branching tree. This algorithm builds a data structure of size O n log( m+n n ) which can be used tosnd the maximum edge weight on the path between leaves ... |

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Citation Context ... edges that forms a spanning tree of G. The current state of the art in MST algorithms shows a gap between theory and practice. The algorithms used in practice are among the oldest network algorithms =-=[2, 5, 10, 13-=-] and are all based on the cut property : a lightest edge leaving a set of nodes can be used for an MST. More specically, Kruskal's algorithm [10] is best for sparse graphs. Its running time is asympt... |

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Citation Context ... edges that forms a spanning tree of G. The current state of the art in MST algorithms shows a gap between theory and practice. The algorithms used in practice are among the oldest network algorithms =-=[2, 5, 10, 13-=-] and are all based on the cut property : a lightest edge leaving a set of nodes can be used for an MST. More specically, Kruskal's algorithm [10] is best for sparse graphs. Its running time is asympt... |