Reachability Querying: Can It Be Even Faster?

As an important graph operator, reachability query has been extensively studied over decades, which is to check whether a vertex can reach another vertex over a large directed graph G with n vertices and m edges. The efforts made in the reported studies have greatly improved the query time of answering reachability queries online, while reducing the offline index construction time to construct an index with a reasonable size given the approach taken, where an entry in an index for a vertex is called a label of the vertex. Among all the work, the recent development of IP (Independent Permutation) employs randomness using k-min-wise independent permutations to process reachability queries, and shows the advantages for both query time and index construction time. In this paper, we propose a new Bloom filter Labeling, denoted as BFL. We show that the probability to answer reachability queries by BFL can be bounded, and BFL has high pruning power to answer more reachability queries directly. We give algorithms and analyze the pruning power of BFL. We conduct extensive studies using 19 large datasets. We show that BFL with an interval label performs best in the index construction time for all 19 cases, and performs best in query time for 16 out of 19 cases.