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Balancing minimum spanning trees and shortestpath trees
 S. Khuller,
 B. Raghavachari,
 N. Young
 … show all 3 hide
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We give a simple algorithm to find a spanning tree that simultaneously approximates a shortestpath 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 shortestpath tree is at most 1+√2γ times the shortestpath 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 bestpossible tradeoff. It can be implemented on a CREW PRAM to run a logarithmic time using one processor per vertex.
Current research supported by NSF Research Initiation Award CCR9307462. This work was done while this author was supported by NSF Grants CCR8906949, CCR9103135, and CCR9111348.
Part of this work was done while this, author was at the University of Maryland Institute for Advanced Computer Studies (UMIACS) and supported by NSF Grants CCR8906949 and CCR9111348.
Communicated by T. Nishizeki.
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 Title
 Balancing minimum spanning trees and shortestpath trees
 Journal

Algorithmica
Volume 14, Issue 4 , pp 305321
 Cover Date
 19951001
 DOI
 10.1007/BF01294129
 Print ISSN
 01784617
 Online ISSN
 14320541
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Minimum spanning trees
 Graph algorithms
 Parallel algorithms
 Shortest paths
 Industry Sectors
 Authors

 S. Khuller ^{(1)}
 B. Raghavachari ^{(2)}
 N. Young ^{(3)}
 Author Affiliations

 1. Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, 20742, College Park, MD, USA
 2. Department of Computer Science, University of Texas at Dallas, Box 830688, 750830688, Richardson, TX, USA
 3. Department of Computer Science, Princeton University, 08544, Princeton, NJ, USA