Efficient Reachability Ratio Computation for 2-Hop Labeling Scheme

Reachability queries processing has been extensively studied during the past decades. Many approaches have followed the line of designing 2-hop labels to ensure acceleration. Considering its index size cannot be bounded, researchers have proposed to use a part of nodes to construct partial 2-hop labels (p2HLs) to cover as much reachability information as possible. We achieved better query performance using p2HLs with a limited index size and index construction time. However, the adoption of p2HLs was based on intuition, and the number of nodes used to generate p2HLs was fixed in advance blindly, without knowing its applicability. In this paper, we focused on the problem of efficiently computing a reachability ratio (RR) in order to obtain RR-aware p2HLs. Here, RR denoted the ratio of the number of reachable queries that could be answered by p2HLs over the total number of reachable queries involved in a given graph. Based on the RR, users could determine whether p2HLs should be used to answer the reachability queries for a given graph and how many nodes should be chosen to generate p2HLs. We discussed the difficulties of RR computation and propose an incremental-partition algorithm for RR computation. Our rich experimental results showed that our algorithm could efficiently obtain the RR and the overall effects on query performance by different p2HLs. Based on the experimental results, we provide our findings on the use p2HLs for a given graph for processing reachability queries.