Efficient algorithms for finding minimum spanning trees in undirected and directed graphs Authors Harold N. Gabow Zvi Galil Columbia University Tel Aviv University Thomas Spencer Rensselaer Polytechnic Inst. Robert E. Tarjan Article

Received: 23 January 1985 Revised: 01 December 1985 DOI :
10.1007/BF02579168

Cite this article as: Gabow, H.N., Galil, Z., Spencer, T. et al. Combinatorica (1986) 6: 109. doi:10.1007/BF02579168
Abstract 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, improved fromO (mβ (m, n )) time, whereβ (m, n )=min {i |log^{(i)} n ≦m/n }. Our minimum spanning tree algorithm for directed graphs runs inO (n logn + m ) time, improved fromO (n log n +m log log log_{(m/n+2)} n ). Both algorithms can be extended to allow a degree constraint at one vertex.

AMS subject classification (1980) 68 B 15 68 C 05 Research supported in part by National Science Foundation Grant MCS-8302648.

Research supported in part by National Science Foundation Grant MCS-8303139.

Research supported in part by National Science Foundation Grant MCS-8300984 and a United States Army Research Office Program Fellowship, DAAG29-83-GO020.

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