, Volume 6, Issue 2, pp 109–122 | Cite as

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

  • Harold N. Gabow
  • Zvi Galil
  • Thomas Spencer
  • Robert E. Tarjan


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((m, n)) time, whereβ(m, n)=min {i|log(i) nm/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 


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Copyright information

© Akadémiai Kiadó 1986

Authors and Affiliations

  • Harold N. Gabow
    • 1
  • Zvi Galil
    • 2
    • 3
  • Thomas Spencer
    • 4
  • Robert E. Tarjan
    • 5
  1. 1.University of ColoradoBoulderUSA
  2. 2.Columbia UniversityNew YorkUSA
  3. 3.Tel Aviv UniversityTel AvivIsrael
  4. 4.Rensselaer Polytechnic Inst.TroyUSA
  5. 5.AT&T Bell LaboratoriesMurray HillUSA

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