Uncertain graph management has been recognized as an important research topic in recent years. In this paper, we first introduce two types of query evaluation problems on uncertain graphs, named expectation query evaluation and threshold query evaluation. Most previous solutions for these problems are based on naive Monte-Carlo (NMC) sampling, which typically result in large variances. To reduce the variance ofNMC, we propose two efficient estimators, calledRSS-IandRSS-IIestimators, based on the idea of recursive stratified sampling (RSS). To further reduce the variances ofRSS-IandRSS-II, we propose a recursivecut-setbased stratified sampling estimator for a particular kind of query evaluation problem. We show that all the proposed estimators are unbiased and their variances are significantly smaller than that ofNMC. Moreover, the time complexity of all the proposed estimators are the same as that ofNMCunder a mild assumption. In addition, we develop an elegant graph simplification technique to further improve the accuracy and running time of our estimators. We also apply the proposed estimators to three different uncertain graph query evaluation problems. Finally, we conduct extensive experiments to evaluate the proposed estimators, and the results show the accuracy, efficiency, and scalability of our estimators.

Random walk based graph sampling has been recognized as a fundamental technique to collect uniform node samples from a large graph. In this paper, we first present a comprehensive analysis of the drawbacks of three widely-used random walk based graph sampling algorithms, called re-weighted random walk (RW) algorithm, Metropolis-Hastings random walk (MH) algorithm and maximum-degree random walk (MD) algorithm. Then, to address the limitations of these algorithms, we propose two general random walk based algorithms, named rejection-controlled Metropolis-Hastings (RCMH) algorithm and generalized maximum-degree random walk (GMD) algorithm. We show that RCMH balances the tradeoff between the limitations of RW and MH, and GMD balances the tradeoff between the drawbacks of RW and MD. To further improve the performance of our algorithms, we integrate the so-called delayed acceptance technique and the non-backtracking random walk technique into RCMH and GMD respectively. We conduct extensive experiments over four real-world datasets, and the results demonstrate the effectiveness of the proposed algorithms.

In this paper, we introduce two types of query evaluation problems on uncertain graphs: expectation query evaluation and threshold query evaluation. Since these two problems are #P-complete, most previous solutions for these problems are based on naive Monte-Carlo (NMC) sampling. However, NMC typically leads to a large variance, which significantly reduces its effectiveness. To overcome this problem, we propose two classes of estimators, called class-I and class-II estimators, based on the idea of stratified sampling. More specifically, we first propose two classes of basic stratified sampling estimators, named BSS-I and BSS-II, which partition the entire population into 2rand r+1 strata by picking r edges respectively. Second, to reduce the variance, we find that both BSS-I and BSS-II can be recursively performed in each stratum. Therefore, we propose two classes of recursive stratified sampling estimators called RSS-I and RSS-II respectively. Third, for a particular kind of problem, we propose two cut-set based stratified sampling estimators, named BCSS and RCSS, to further improve the accuracy of the class-I and class-II estimators. For all the proposed estimators, we prove that they are unbiased and their variances are significantly smaller than that of NMC. Moreover, the time complexity of all the proposed estimators are the same as the time complexity of NMC under a mild assumption. In addition, we also apply the proposed estimators to influence function evaluation and expected-reliable distance query problem, which are two instances of the query evaluation problems on uncertain graphs. Finally, we conduct extensive experiments to evaluate our estimators, and the results demonstrate the efficiency, accuracy, and scalability of the proposed estimators.