# Balancing minimum spanning trees and shortest-path trees

Article

- Received:
- Revised:

DOI: 10.1007/BF01294129

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

## Abstract

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 a*γ*>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