, Volume 14, Issue 4, pp 305–321

Balancing minimum spanning trees and shortest-path trees


  • S. Khuller
    • Department of Computer Science and Institute for Advanced Computer StudiesUniversity of Maryland
  • B. Raghavachari
    • Department of Computer ScienceUniversity of Texas at Dallas
  • N. Young
    • Department of Computer SciencePrinceton University

DOI: 10.1007/BF01294129

Cite this article as:
Khuller, S., Raghavachari, B. & Young, N. Algorithmica (1995) 14: 305. doi:10.1007/BF01294129


We give a simple algorithm to find a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous tradeoff: given the two trees and aγ>0, the algorithm returns a spanning tree in which the distance between any vertex and the root of the shortest-path tree is at most 1+√2γ times the shortest-path distance, and yet the total weight of the tree is at most 1+√2/γ times the weight of a minimum spanning tree. Our algorithm runs in linear time and obtains the best-possible tradeoff. It can be implemented on a CREW PRAM to run a logarithmic time using one processor per vertex.

Key words

Minimum spanning treesGraph algorithmsParallel algorithmsShortest paths

Copyright information

© Springer-Verlag New York Inc. 1995