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.

Efficiently processing queries against very large graphs is an important research topic largely driven by emerging real world applications, as diverse as XML databases, GIS, web mining, social network analysis, ontologies, and bioinformatics. In particular, graph reachability has attracted a lot of research attention as reachability queries are not only common on graph databases, but they also serve as fundamental operations for many other graph queries. The main idea behind answering reachability queries in graphs is to build indices based on reachability labels. Essentially, each vertex in the graph is assigned with certain labels such that the reachability between any two vertices can be determined by their labels. Several approaches have been proposed for building these reachability labels; among them are interval labeling (tree cover) and 2-hop labeling. However, due to the large number of vertices in many real world graphs (some graphs can easily contain millions of vertices), the computational cost and (index) size of the labels using existing methods would prove too expensive to be practical. In this paper, we introduce a novel graph structure, referred to as pathtree, to help labeling very large graphs. The path-tree cover is a spanning subgraph of G in a tree shape. We demonstrate both analytically and empirically the effectiveness of our new approaches.

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A reachability oracle (or hop labeling) assigns each vertex v two sets of vertices: Lout(v) and Lin (v), such that u reaches v iff Lout(u) ∩ Lin(v) = ∅. Despite their simplicity and elegance, reachability oracles have failed to achieve efficiency in more than ten years since their introduction: the main problem is high construction cost, which stems from a set-cover framework and the need to materialize transitive closure. In this paper, we present two simple and efficient labeling algorithms, Hierarchical-Labeling and Distribution-Labeling, which can work on massive real-world graphs: their construction time is an order of magnitude faster than the setcover based labeling approach, and transitive closure materialization is not needed. On large graphs, their index sizes and their query performance can now beat the state-of-the-art transitive closure compression and online search approaches. large graphs, their index sizes and their query performance beat the state-of-the-art transitive closure compression and online search approaches [21,35,23,35,12,37]. Using these two algorithms, the power of hop labeling is finally unleashed and a fast, compact and scalable reachability oracle becomes a reality.

Urban traffic gridlock is a familiar scene. At the same time, the mean occupancy rate of personal vehicle trips in the United States is only 1.6 persons per vehicle mile. Ridesharing has the potential to solve many environmental, congestion, pollution, and energy problems. In this paper, we introduce the problem of large scale real-time ridesharing with service guarantee on road networks. Trip requests are dynamically matched to vehicles while trip waiting and service time constraints are satisfied. We first propose two scheduling algorithms: a branch-and-bound algorithm and an integer programing algorithm. However, these algorithms do not adapt well to the dynamic nature of the ridesharing problem. Thus, we propose kinetic tree algorithms which are better suited to efficient scheduling of dynamic requests and adjust routes on-the-fly. We perform experiments on a large Shanghai taxi dataset. Results show that the kinetic tree algorithms outperform other algorithms significantly.

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A key task in analyzing social networks and other complex networks is role analysis: describing and categorizing nodes by how they interact with other nodes. Two nodes have the same role if they interact with equivalent sets of neighbors. The most fundamental role equivalence is automorphic equivalence. Unfortunately, the fastest algorithm known for graph automorphism is nonpolynomial. Moreover, since exact equivalence is rare, a more meaningful task is measuring the role similarity between any two nodes. This task is closely related to the link-based similarity problem that SimRank addresses. However, SimRank and other existing simliarity measures are not sufficient because they do not guarantee to recognize automorphically or structurally equivalent nodes. This paper makes two contributions. First, we present and justify several axiomatic properties necessary for a role similarity measure or metric. Second, we present RoleSim, a role similarity metric which satisfies these axioms and which can be computed with a simple iterative algorithm. We rigorously prove that RoleSim satisfies all the axiomatic properties and demonstrate its superior interpretative power on both synthetic and real datasets.

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