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Balancing minimum spanning trees and shortest-path trees

  • Author(s): Khuller, S
  • Raghavachari, B
  • Young, N
  • et al.

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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 tradeoff: given the two trees and a γ>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+√2γ times the shortest-path distance, and yet the total weight of the tree is at most 1+√2/γ times the weight of a minimum spanning tree. Our algorithm runs in linear time and obtains the best-possible tradeoff. It can be implemented on a CREW PRAM to run a logarithmic time using one processor per vertex. © 1995 Springer-Verlag New York Inc.

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