Efficiently Answering Probability Threshold-Based Shortest Path Queries over Uncertain Graphs

Yuan, Ye; Chen, Lei; Wang, Guoren

doi:10.1007/978-3-642-12026-8_14

Cited by 57 publications

(44 citation statements)

References 18 publications

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“…Managing and mining uncertain graphs has recently attracted much attention in the database and data mining research community [13,23,24,25]. Especially, Potamias et.…”

Section: Related Workmentioning

confidence: 99%

“…For instance, in [23], the authors studied to discover the shortest paths in uncertain graph with the condition that each such shortest path has probability no less than certain threshold. Inspired by this, in Appendix G, we describe a simple extension of DCR (Distance-Constraint Reachability) query and discuss how our approaches can be applied to the new problem.…”

Section: Related Workmentioning

confidence: 99%

“…Here, we consider strengthening the DCR (Distance-Constraint Reachability) query with an additional constraint introduced in [23]. Recall that a s-t path in G with length less than or equal to distance constraint d is referred to as a d-path between s and t. If there is a d-path between s and t, then vertex t is d-reachable from vertex s in graph G, i.e., dis(s, t|G) ≤ d. If there is no d-path from s to t, then, t is not d-reachable from s (dis(s, t|G) > d).…”

Section: Appendixmentioning

confidence: 99%

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Distance-constraint reachability computation in uncertain graphs

et al. 2011

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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.

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“…Managing and mining uncertain graphs has recently attracted much attention in the database and data mining research community [13,23,24,25]. Especially, Potamias et.…”

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

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Distance-constraint reachability computation in uncertain graphs

et al. 2011

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“…Each possible subgraph of the uncertain graph is called implicated graph. Their research mainly focus on graph mining [10]- [12], graph queries [13]- [15] and basic graph structure [16], [17].…”

Section: Introductionmentioning

confidence: 99%

Reliability Evaluation of the Minimum Spanning Tree on Uncertain Graph

Tang¹,

Liu²,

Wen³

2015

JCP

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Abstract:Minimum spanning tree is a minimum-cost spanning tree connecting the whole network, but it couldn't be directly obtained on uncertain graph. In this paper, we define the reliability as the existence probability of all minimum spanning trees and present an algorithm for evaluating reliability of the minimum spanning tree on uncertain graph. The time complexity of the algorithm is O(Nmn), where n, m and N stand for the number of vertices, edges and minimum spanning trees, respectively. Because this algorithm spends more time finding minimum spanning tree, we propose an improved algorithm whose time complexity is O(Nm). The improved algorithm uses disjoint set data structure so that the average time complexity on finding a new minimum spanning tree is O(m/n). The two algorithms are analyzed in detail and the experiment results agree with theoretical analysis.

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“…Most existing works on graph uncertainty consider existence uncertainty, where a given edge exists probabilistically and the existence probabilities of the individual edges are assumed to be independent from each other [2,10,16,20,26,29]. In practice, however, this assumption does not always hold: we may be aware of the existence of an edge, but we may not know between which pairs of nodes the edge exists.…”

mentioning

confidence: 99%

Personalized PageRank in Uncertain Graphs with Mutually Exclusive Edges

Kim

Candan

et al. 2017

Proceedings of the 40th International ACM SIGIR Conference on Research and Development in Information Retrieval

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Measures of node ranking, such as personalized PageRank, are utilized in many web and social-network based prediction and recommendation applications. Despite their e ectiveness when the underlying graph is certain, however, these measures become di cult to apply in the presence of uncertainties, as they are not designed for graphs that include uncertain information, such as edges that mutually exclude each other. While there are several ways to naively extend existing techniques (such as trying to encode uncertainties as edge weights or computing all possible scenarios), as we discuss in this paper, these either lead to large degrees of errors or are very expensive to compute, as the number of possible worlds can grow exponentially with the amount of uncertainty. To tackle with this challenge, in this paper, we propose an e cient Uncertain Personalized PageRank (UPPR) algorithm to approximately compute personalized PageRank values on an uncertain graph with edge uncertainties. UPPR avoids enumeration of all possible worlds, yet it is able to achieve comparable accuracy by carefully encoding edge uncertainties in a data structure that leads to fast approximations. Experimental results show that UPPR is very e cient in terms of execution time and its accuracy is comparable or be er than more costly alternatives.

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Efficiently Answering Probability Threshold-Based Shortest Path Queries over Uncertain Graphs

Cited by 57 publications

References 18 publications

Distance-constraint reachability computation in uncertain graphs

Distance-constraint reachability computation in uncertain graphs

Reliability Evaluation of the Minimum Spanning Tree on Uncertain Graph

Personalized PageRank in Uncertain Graphs with Mutually Exclusive Edges

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