A unifying framework for ℓ 0 -sampling algorithms

The problem of building an ℓ 0 -sampler is to sample near-uniformly from the support set of a dynamic multiset. This problem has a variety of applications within data analysis, computational geometry and graph algorithms. In this paper, we abstract a set of steps for building an ℓ 0 -sampler, based on sampling, recovery and selection. We analyze the implementation of an ℓ 0 -sampler within this framework, and show how prior constructions of ℓ 0 -samplers can all be expressed in terms of these steps. Our experimental contribution is to provide a first detailed study of the accuracy and computational cost of ℓ 0 -samplers.