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 λ, find the smallest value of λ such that the graph contains no negative-weight cycles.
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Eppstein, D., Wortman, K.A. (2009). Optimal Embedding into Star Metrics. In: Dehne, F., Gavrilova, M., Sack, JR., Tóth , C.D. (eds) Algorithms and Data Structures. WADS 2009. Lecture Notes in Computer Science, vol 5664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03367-4_26
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DOI: https://doi.org/10.1007/978-3-642-03367-4_26
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