Decentralized Graph Processing for Reachability Queries

Joël Mathys, Robin Fritsch, Roger Wattenhofer

Abstract: Answering queries on large graphs is an essential part of data processing. In this paper, we focus on determining reachability between vertices. We propose a labeling scheme which is inherently distributed and can be processed in parallel. We study what properties make it difficult to find a good reachability labeling scheme for directed graphs. We focus on the genus of a graph. For graphs of bounded genus g, we design a labeling scheme of length $$\mathcal {O}(g\log n + {\log }^{2}{n})$$ . We also prove that no labeling schemes with labels shorter than $$\varOmega (\sqrt{g})$$ exist for this graph class.