Model Counting Meets Distinct Elements

Constraint Satisfaction Problems (CSPs) 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 CSPs and the computation of the number of distinct elements in a data stream, also known as the zeroth frequency moment (F0) of a data stream. Our investigations lead us to observe striking similarity in the core techniques employed in the algorithmic frameworks that have evolved separately for model counting and distinct elements computation. We design a recipe for the translation of algorithms developed for distinct elements estimation to that of model counting, resulting in new algorithms for model counting. 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 distinct elements 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. Constraint Satisfaction Problems (CSP's) and a data stream model are two core themes in computer science with a diverse set of applications in topics including probabilistic reasoning, networks, databases, and verification. Model counting and computation of zeroth frequency moment (F0) are fundamental problems for CSPs and a data stream model respectively. This paper is motivated by our observation that despite the usage of similar algorithmic techniques for the two problems, the developments in the two communities have, surprisingly, evolved separately, and rarely has a paper from one community been cited by the other.