Balancing minimum spanning trees and shortest-path trees

Samir Khuller*, B. Raghavachari, N. Young

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

157 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)305-321
Number of pages17
JournalAlgorithmica
Volume14
Issue number4
DOIs
StatePublished - Oct 1995

Keywords

  • Graph algorithms
  • Minimum spanning trees
  • Parallel algorithms
  • Shortest paths

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

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