In-database connected component analysis

We describe a Big Data-practical, SQL-implementable algorithm for efficiently determining connected components for graph data stored in a Massively Parallel Processing (MPP) relational database. The algorithm described is a linear-space, randomised algorithm, always terminating with the correct answer but subject to a stochastic running time, such that for any \(\epsilon>0\) and any input graph \(G=\langle V, E \rangle\) the algorithm terminates after \(\mathop{\text{O}}(\log |V|)\) SQL queries with probability of at least \(1-\epsilon\), which we show empirically to translate to a quasi-linear runtime in practice.