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Balancing Minimum Spanning Trees and Shortest-Path Trees

By Samir Khuller


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 trade-off: given the two trees and a fl? 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 + p2fl times the shortest-path distance, and yet the total weight of the tree is at most 1 + p2=fl times the weight of a minimum spanning tree. Our algorithm runs in linear time and obtains the best-possible trade-off. It can be implemented on a CREW PRAM to run in logarithmic time using one processor per vertex

Topics: minimum spanning trees, graph algorithms, parallel algorithms, shortest paths
Year: 1995
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