Random Rates for 0-Extension and Low-Diameter Decompositions

Abstract: Consider the problem of partitioning an arbitrary metric space into pieces of diameter at most \Delta, such every pair of points is separated with relatively low probability. We propose a rate-based algorithm inspired by multiplicatively-weighted Voronoi diagrams, and prove it has optimal trade-offs. This also gives us another logarithmic approximation algorithm for the 0-extension problem.