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Balancing Minimum Spanning and Shortest Path Trees

Samir Khuller·Balaji Raghavachari·Neal E. Young
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Abstract

This paper give a simple linear-time algorithm that, given a weighted digraph, finds 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 epsilon > 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+epsilon times the shortest-path distance, and yet the total weight of the tree is at most 1+2/epsilon times the weight of a minimum spanning tree. This is the best tradeoff possible. The paper also describes a fast parallel implementation.

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Samir Khuller, Balaji Raghavachari, Neal E. Young. 2002-05-18. Balancing Minimum Spanning and Shortest Path Trees. https://doi.org/10.1007/bf01294129

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