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Balancing minimum spanning trees and shortest-path trees

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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 aγ>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.

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Communicated by T. Nishizeki.

Current research supported by NSF Research Initiation Award CCR-9307462. This work was done while this author was supported by NSF Grants CCR-8906949, CCR-9103135, and CCR-9111348.

Part of this work was done while this, author was at the University of Maryland Institute for Advanced Computer Studies (UMIACS) and supported by NSF Grants CCR-8906949 and CCR-9111348.

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Khuller, S., Raghavachari, B. & Young, N. Balancing minimum spanning trees and shortest-path trees. Algorithmica 14, 305–321 (1995).

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