Tapping the Link between Algorithmic Model Counting and Streaming: Technical Perspective

Abstract

algorithms for F0 estimation to algorithms for model counting. The authors also show a partial converse, namely, by framing F0 estimation as a special case of model counting, the authors obtain a very general algorithm for F0 estimation and variants. The resulting algorithms can be used to select a minimum cost query plan in database design and are also a key tool for detecting denial-of-service attacks in network monitoring. The starting point of the paper is the observation that a hashing-based technique for model counting1,3 uses the same techniques as an F0 estimation data stream algorithm.2 The idea behind both is to reduce the counting problem to a detection problem. For model counting, one chooses random subsets of possible solutions of geometrically varying size and checks if there is any satisfying assignment to φ in each subset. For F0 estimation in data streams, one chooses random subsets of universe items of geometrically varying size and checks if there is an item in one’s subset that occurs in the stream. In both cases, by finding the size of the smallest set for which there is a satisfying assignment (for model counting) or an element occurring in the stream (for F0 estimation), one can scale back up by the reciprocal of that set’s size to obtain a decent approximation to the number of solutions (for model counting) or number of distinct elements (for data streams).