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This paper give a simple linear-time algorithm that, given a weighteddigraph, finds a spanning tree that simultaneously approximates a shortest-pathtree and a minimum spanning tree. The algorithm provides a continuoustrade-off: given the two trees and epsilon > 0, the algorithm returns aspanning tree in which the distance between any vertex and the root of theshortest-path tree is at most 1+epsilon times the shortest-path distance, andyet the total weight of the tree is at most 1+2/epsilon times the weight of aminimum spanning tree. This is the best tradeoff possible. The paper alsodescribes a fast parallel implementation.Comment: conference version: ACM-SIAM Symposium on Discrete Algorithms (1993

Balancing minimum spanning trees and shortest-path trees