Efficient Reachability Ratio Computation for 2-hop Labeling Scheme

As one of the fundamental graph operations, reachability queries processing has been extensively studied during the past decades. Many approaches followed the line of designing 2-hop labels to make acceleration. Considering that the index size cannot be bounded when using all nodes to construct 2-hop labels, researchers proposed to use a part of important nodes to construct 2-hop labels (partial 2-hop labels) to cover as much reachability information as possible. Then, we may achieve better query performance with limited index size and index construction time. However, partial 2-hop labels do not always perform well on different graphs. In this paper, we focus on the problem of how to efficiently compute reachability ratio, such that to help users determine whether partial 2-hop labels should be used to answer reachability queries for the given graph. Intuitively, reachability ratio denotes the ratio of the number of reachable queries that can be answered by partial 2-hop labels over the total number of reachable queries involved in the given graph. We discuss the difficulties of reachability ratio computation, and propose an incremental-partition algorithm for reachability ratio computation. We show by rich experimental results that our algorithm can efficiently get the result of reachability ratio, and show how the overall query performance is affected by different partial 2-hop labels. Based on the experimental results, we give out our findings on whether partial 2-hop labels should be used to the given graph for reachability queries processing.