Efficient Probabilistic Truss Indexing on Uncertain Graphs

Networks in many real-world applications come with an inherent uncertainty in their structure, due to e.g., noisy measurements, inference and prediction models, or for privacy purposes. Modeling and analyzing uncertain graphs has attracted a great deal of attention. Among the various graph analytic tasks studied, the extraction of dense substructures, such as cores or trusses, has a central role. In this paper, we study the problem of (k, γ )-truss indexing and querying over an uncertain graph G. A (k, γ )-truss is the largest subgraph of G, such that the probability of each edge being contained in at least k -2 triangles is no less than γ . Our first proposal, CPT-index, keeps all the (k, γ )-trusses: retrieval for any given k and γ can be executed in an optimal linear time w.r.t. the graph size of the queried (k, γ )-truss. We develop a bottom-up CPT-index construction scheme and an improved algorithm for fast CPT-index construction using top-down graph partitions. For trading off between (k, γ )-truss offline indexing and online querying, we further develop an approximate indexing approach (ϵ, ∆ r )-APX equipped with two parameters, ϵ and ∆ r , that govern tolerated errors. Extensive experiments using large-scale uncertain graphs with 261 million edges validate the efficiency of our proposed indexing and querying algorithms against state-of-the-art methods.