When is Approximate Counting for Conjunctive Queries Tractable?

Threshold Queries in Theory and in the Wild

“…However, when the problem is relaxed to approximate counting, tractability comes easier. A very recent paper [3] shows under similar technical assumptions that a class of CQs admits a fully polynomial randomized approximation scheme for counting answers iff the queries in the class have bounded tree-width; that is, the characterization is just like for Boolean evaluation. In this work, we consider a very different relaxation -counting exactly, but only up to a given thresholdand we also show tractability for CQs of bounded tree-width.…”

“…A different approach to non-acyclic full CQs [16] provides a uniform sampling algorithm with expected running time proportional to the product of the database size and the ratio between the AGM bound [5] on the number of answers to the underlying full CQ and the actual number of answers of the input query; this is incomparable to constant-time sampling after polynomial-time preprocessing, offered by our approach. Finally, Arenas et al [3] show that, under certain complexity-theoretical assumptions, a structural class of CQs admits a fully polynomial-time almost uniform sampler iff the queries in the class have bounded tree-width. Here, almost uniform means that the algorithm approximates the uniform distribution up to a multiplicative error; this is a weaker notion than uniform sampling.…”