# Efficient algorithms for finding minimum spanning trees in undirected and directed graphs

@article{Gabow1986EfficientAF, title={Efficient algorithms for finding minimum spanning trees in undirected and directed graphs}, author={Harold N. Gabow and Zvi Galil and Thomas H. Spencer and Robert E. Tarjan}, journal={Combinatorica}, year={1986}, volume={6}, pages={109-122} }

Recently, Fredman and Tarjan invented a new, especially efficient form of heap (priority queue). Their data structure, theFibonacci heap (or F-heap) supports arbitrary deletion inO(logn) amortized time and other heap operations inO(1) amortized time. In this paper we use F-heaps to obtain fast algorithms for finding minimum spanning trees in undirected and directed graphs. For an undirected graph containingn vertices andm edges, our minimum spanning tree algorithm runs inO(m logβ (m, n)) time…

## 522 Citations

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The Gabow and Tarjan problem, i.e., finding a path between a given source and a given target in a weighted directed graph whose largest edge weight is minimized, as well as the Bottleneck spanning tree problem, can be solved deterministically in O(m log∗ n) time.

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An efficient algorithm for sensitivity analysis of minimum spanning trees which requires O(log n) time and O(max{m, n/sup 2//log n}) processors is presented and has better performance when G is sparse.

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A slightly improved randomized algorithm for the Bottleneck Path problem and the Bott bottleneck spanning tree problem, observing that in the word-RAM model, both problems can be solved deterministically in O(m) time.

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The fusion tree method is extended to develop a linear-time algorithm for the minimum spanning tree problem and an O(m+n log n/log log n) implementation of Dijkstra's shortest-path algorithm for a…

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We describe an efficient implementation of Edmonds’ algorithm for finding minimum directed spanning trees in directed graphs. 1 Minimum Directed Spanning Trees Let G = (V,E,w) be a weighted directed…

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