Optimal Embedding into Star Metrics

Authors:
David Eppstein;Kevin A. Wortman
Affiliations:
Department of Computer Science, Universitiy of California, Irvine,;Department of Computer Science, Universitiy of California, Irvine,
Venue:
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Year:
2009

Citing 7
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Abstract

We present an O (n 3 log2 n )-time algorithm for the following problem: given a finite metric space X , create a star-topology network with the points of X as its leaves, such that the distances in the star are at least as large as in X , with minimum dilation. As part of our algorithm, we solve in the same time bound the parametric negative cycle detection problem : given a directed graph with edge weights that are increasing linear functions of a parameter *** , find the smallest value of *** such that the graph contains no negative-weight cycles.