Random Rates for 0-Extension and Low-Diameter Decompositions

TL;DR

This paper introduces a rate-based algorithm for partitioning metric spaces into low-diameter pieces with low separation probability, achieving optimal trade-offs and improving approximation for the 0-extension problem.

Contribution

It presents a novel rate-based algorithm inspired by weighted Voronoi diagrams that offers optimal trade-offs for low-diameter decompositions and enhances approximation for 0-extension.

Findings

Achieves optimal trade-offs in low-diameter decompositions.

Provides a logarithmic approximation algorithm for 0-extension.

Introduces a new rate-based approach inspired by Voronoi diagrams.

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.