Threshold-Based Shortest Path Query over Large Correlated Uncertain Graphs

Abstract

With the popularity of uncertain data, queries over uncertain graphs have become a hot topic in the database community. As one of the important queries, the shortest path query over an uncertain graph has attracted much attention of researchers due to its wide applications. Although there are some efficient solutions addressing this problem, all existing models ignore an important property existing in uncertain graphs: the correlation among the edges sharing the same vertex. In this paper, we apply Markov network to model the hidden correlation in uncertain graphs and compute the shortest path. Unfortunately, calculating the shortest path and corresponding probability over uncertain graphs modeled by Markov networks is a #P-hard problem. Thus, we propose a filtering-and-verification framework to accelerate the queries. In the filtering phase, we design a probabilistic shortest path index based on vertex cuts and blocks of a graph. We find a series of upper bounds and prune the vertices and edges whose upper bounds of the shortest path probability are lower than the threshold. By carefully picking up the blocks and vertex cuts, the index is optimized to have the maximum pruning capability, so that we can filter a large number of vertices which make no contribution to the final shortest path query results. In the verification phase, we develop an efficient sampling algorithm to determine the final query answers. Finally, we verify the efficiency and effectiveness of our solutions with extensive experiments.

Shortest paths and centrality in uncertain networks

“…Several variants of shortest-path queries over uncertain graphs have been studied in the literature. Work in [12,13,62] investigates threshold-based shortest-path queries in uncertain graphs, i.e., the problem of finding all paths having shortest-path probability larger than a predefined threshold. In particular, [12,13] consider a different uncertain graph model with correlation.…”

“…Work in [12,13,62] investigates threshold-based shortest-path queries in uncertain graphs, i.e., the problem of finding all paths having shortest-path probability larger than a predefined threshold. In particular, [12,13] consider a different uncertain graph model with correlation. The work closest to ours is probably [63], which considers MPSP queries as we do, but it does not provide any hardness result or any accuracy guarantee.…”

“…In [63], similar to [13,62], a filtering-and-verification framework is used, which enumerates paths between the two given nodes in increasing order of length, without considering edges' probabilities, till a termination criterion is achieved. Among the candidate paths generated, a sampling method is applied (e.g., the Luby-Karp algorithm [28]) to approximately measure each candidate path's probability of being the shortest path.…”

Conditional Reliability in Uncertain Graphs

“…Uncertain graphs with correlated edge probabilities. Although the bulk of the literature on uncertain graphs assumes edges to be independent of one another [7], [10], [23], [26], some works deal with correlated edge probabilities, where the existence of an edge may depend on the existence of other edges in the graph (typically, edges sharing an end node) [13], [14], [32], [36]. Another model that differs from the classic one is the one adopted by Liu et.…”

Efficient optimization of network metrics in large uncertain graphs

“…Several variants of shortest path queries over uncertain graphs have been studied in the literature. Work in [210,40,39] investigates threshold-based shortest path queries in uncertain graphs, i.e. the problem of finding all paths having shortest path probabilities larger than a predefined threshold.…”