Compact reachability labeling for graph-structured data

Testing reachability between nodes in a graph is a well-known problem with many important applications, including knowledge representation, program analysis, and more recently, biological and ontology databases inferencing as well as XML query processing. Various approaches have been proposed to encode graph reachability information using node labeling schemes, but most existing schemes only work well for specific types of graphs. In this paper, we propose a novel approach, HLSS(Hierarchical Labeling of Sub-Structures), which identifies different types of substructures within a graph and encodes them using techniques suitable to the characteristics of each of them. We implement HLSS with an efficient two-phase algorithm, where the first phase identifies and encodes strongly connected components as well as tree substructures, and the second phase encodes the remaining reachability relationships by compressing dense rectangular submatrices in the transitive closure matrix. For the important subproblem of finding densest submatrices, we demonstrate the hardness of the problem and propose several practical algorithms. Experiments show that HLSS handles different types of graphs well, while existing approaches fall prey to graphs with substructures they are not designed to handle.