Balancing Minimum Spanning and Shortest Path Trees
Data Structures and Algorithms
2015-06-02 v1 Discrete Mathematics
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.
Cite
@article{arxiv.cs/0205045,
title = {Balancing Minimum Spanning and Shortest Path Trees},
author = {Samir Khuller and Balaji Raghavachari and Neal E. Young},
journal= {arXiv preprint arXiv:cs/0205045},
year = {2015}
}
Comments
conference version: ACM-SIAM Symposium on Discrete Algorithms (1993)