neal young / Khuller95Balancing

  • publication/Khuller95Balancing.png This paper has a simple linear-time 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 \(\epsilon > 0\), 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 trade-off possible.
    Journal version of [1993].

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