DistanceConstraint Reachability Computation in Uncertain Graphs∗ Ruoming Jin† Lin Liu† Bolin Ding‡ Haixun Wang§ † Kent State University ‡ UIUC § Microsoft Research Asia Kent, OH, USA Urbana, IL, USA Beijing, China {jin, lliu}@cs.kent.edu
[email protected] [email protected] ABSTRACT Driven by the emerging network applications, querying and mining uncertain graphs has become increasingly important. In this paper, we investigate a fundamental problem concerning uncertain graphs, (a) Uncertain Graph G. (b) G with 0.0009072. which we call the distance-constraint reachability (DCR) problem: 1 Given two vertices s and t, what is the probability that the distance from s to t is less than or equal to a user-defined threshold d in the uncertain graph? Since this problem is #P-Complete, we focus on efficiently and accurately approximating DCR online. Our main results include two new estimators for the probabilistic reachabil- (c) G2 with 0.0009072. (d) G3 with 0.0006048. ity. One is a Horvitz-Thomson type estimator based on the unequal Figure 1: Running Example. probabilistic sampling scheme, and the other is a novel recursive vertex can reach another one, is the basis for a variety of databases sampling estimator, which effectively combines a deterministic re- (XML/RDF) and network applications (e.g., social and biological cursive computational procedure with a sampling process to boost networks) [8, 22]. For uncertain graphs, reachability is not a sim- the estimation accuracy. Both estimators can produce much smaller ple Yes/No question, but instead, a probabilistic one. Specifically, variance than the direct sampling estimator, which considers each reachability from vertex s to vertex t is expressed as the overall trial to be either 1 or 0.