Distance-constraint reachability computation in uncertain graphs

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, which we call the distance-constraint reachability (DCR) problem: 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 reachability. One is a Horvitz-Thomson type estimator based on the unequal probabilistic sampling scheme, and the other is a novel recursive sampling estimator, which effectively combines a deterministic recursive computational procedure with a sampling process to boost the estimation accuracy. Both estimators can produce much smaller variance than the direct sampling estimator, which considers each trial to be either 1 or 0. We also present methods to make these estimators more computationally efficient. The comprehensive experiment evaluation on both real and synthetic datasets demonstrates the efficiency and accuracy of our new estimators.

Reachability querying: an independent permutation labeling approach

“…Jin et al [17] propose SCARAB as a general framework to represent a reachability backbone, denoted as a graph B(V, E), for a graph G. …”

“…We denote our approach as IP+ (Algorithm 2), which uses IP labels with two additional Level labels and HVLabel. And we compare IP+ with the state-of-the-art reachability approaches including GRAIL [29], GRAIL * [30], ScaGRAIL [17,29], PWAH8 [27], TF-Label [10], HL [19], DL [19], and Ferrari [24]. Here, GRAIL and Ferrari are two state-of-art Label+G approaches, and their index size and construction time are in linear.…”

“…We test Ferrari using the Ferrari-G index given in [24], because Ferrari-G is scalable to handle massive-scale graphs. GRAIL * is the improved version of GRAIL [30] and ScaGRAIL is the implementation of GRAIL in the SCARAB framework [17]. 1 We also test the Label-Only approaches.…”

“…Real Datasets: We use all large datasets used in the recent works [29,30,17,27,10,19,24]. Here, citeseer, citeseerx (citeseerx.…”

“…uniprotenc22m, uniprotenc100m, and uniprotenc150m are subgraphs of the complete RDF graph of UniProt. mapped-100K and mapped-1M are two datasets used in [17,19]. email is a DAG of the communication network email-EuAll.…”