Join and subgraph sampling under degree constraints

This article studies two problems related to sampling from the results of database queries. The first one is to uniformly sample a tuple from the result of a join obeying an acyclic set of degree constraints (the join itself need not be acyclic). The second is to uniformly sample a given subgraph pattern's occurrence (the pattern may contain cycles) in a directed data graph. It is shown that, after a linear expected-time preprocessing, both problems admit an algorithm drawing a sample in $O(\mathrm{polymat}/\max \{1,\mathrm{OUT}\left\}\right)$ expected time, where OUT and polymat are the “full result size” and “polymatroid bound” of the underlying problem, respectively (assuming data complexity). These results are derived with a new sampling algorithm for the former problem and a new graph-theoretic theorem for the latter.