Maximum Gradient Embeddings and Monotone Clustering
نویسندگان
چکیده
Let (X, dX) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f : X → T such that for every x ∈ X, ED [ max y∈X\{x} dT ( f (x), f (y)) dX(x, y) ] ≤ C(log n), where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.
منابع مشابه
A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems
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عنوان ژورنال:
- Combinatorica
دوره 30 شماره
صفحات -
تاریخ انتشار 2007