Model Counting meets F0 Estimation

Abstract

Constraint satisfaction problems (CSP’s) and data stream models are two powerful abstractions to capture a wide variety of problems arising in different domains of computer science. Developments in the two communities have mostly occurred independently and with little interaction between them. In this work, we seek to investigate whether bridging the seeming communication gap between the two communities may pave the way to richer fundamental insights. To this end, we focus on two foundational problems: model counting for CSP’s and computation of zeroth frequency moments (F₀) for data streams.

Our investigations lead us to observe a striking similarity in the core techniques employed in the algorithmic frameworks that have evolved separately for model counting and F₀ computation. We design a recipe for translating algorithms developed for F₀ estimation to model counting, resulting in new algorithms for model counting. We also provide a recipe for transforming sampling algorithm over streams to constraint sampling algorithms. We then observe that algorithms in the context of distributed streaming can be transformed into distributed algorithms for model counting. We next turn our attention to viewing streaming from the lens of counting and show that framing F₀ estimation as a special case of #DNF counting allows us to obtain a general recipe for a rich class of streaming problems, which had been subjected to case-specific analysis in prior works. In particular, our view yields an algorithm for multidimensional range efficient F₀ estimation with a simpler analysis.