Many online social networks feature restrictive web interfaces which only allow the query of a user's local neighborhood through the interface. To enable analytics over such an online social network through its restrictive web interface, many recent efforts reuse the existing Markov Chain Monte Carlo methods such as random walks to sample the social network and support analytics based on the samples. The problem with such an approach, however, is the large amount of queries often required (i.e., a long "mixing time") for a random walk to reach a desired (stationary) sampling distribution. In this paper, we consider a novel problem of enabling a faster random walk over online social networks by "rewiring" the social network on-the-fly. Specifically, we develop Modified TOpology (MTO)-Sampler which, by using only information exposed by the restrictive web interface, constructs a "virtual" overlay topology of the social network while performing a random walk, and ensures that the random walk follows the modified overlay topology rather than the original one. We show that MTO-Sampler not only provably enhances the efficiency of sampling, but also achieves significant savings on query cost over real-world online social networks such as Google Plus, Epinion etc.
With global topology, @cite_12 discussed sampling techniques like random node, random edge, random subgraph in large graphs. @cite_22 introduced Albatross sampling which combines random jump and MHRW. @cite_26 also demonstrated true uniform sampling method among the users' id as ground-truth".
@cite_26 @cite_22 @cite_12
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In this paper, we propose an efficient method to detect the underlying structures in data. The same as RANSAC, we randomly sample MSSs (minimal size samples) and generate hypotheses. Instead of analyzing each hypothesis separately, the consensus information in all hypotheses is naturally fused into a hypergraph, called random consensus graph, with real structures corresponding to its dense subgraphs. The sampling process is essentially a progressive refinement procedure of the random consensus graph. Due to the huge number of hyperedges, it is generally inefficient to detect dense subgraphs on random consensus graphs. To overcome this issue, we construct a pairwise graph which approximately retains the dense subgraphs of the random consensus graph. The underlying structures are then revealed by detecting the dense subgraphs of the pair-wise graph. Since our method fuses information from all hypotheses, it can robustly detect structures even under a small number of MSSs. The graph framework enables our method to simultaneously discover multiple structures. Besides, our method is very efficient, and scales well for large scale problems. Extensive experiments illustrate the superiority of our proposed method over previous approaches, achieving several orders of magnitude speedup along with satisfactory accuracy and robustness. Graph sampling via crawling has been actively considered as a generic and important tool for collecting uniform node samples so as to consistently estimate and uncover various characteristics of complex networks. The so-called simple random walk with re-weighting (SRW-rw) and Metropolis-Hastings (MH) algorithm have been popular in the literature for such unbiased graph sampling. However, an unavoidable downside of their core random walks -- slow diffusion over the space, can cause poor estimation accuracy. In this paper, we propose non-backtracking random walk with re-weighting (NBRW-rw) and MH algorithm with delayed acceptance (MHDA) which are theoretically guaranteed to achieve, at almost no additional cost, not only unbiased graph sampling but also higher efficiency (smaller asymptotic variance of the resulting unbiased estimators) than the SRW-rw and the MH algorithm, respectively. In particular, a remarkable feature of the MHDA is its applicability for any non-uniform node sampling like the MH algorithm, but ensuring better sampling efficiency than the MH algorithm. We also provide simulation results to confirm our theoretical findings. We consider the task of topology discovery of sparse random graphs using end-to-end random measurements (e.g., delay) between a subset of nodes, referred to as the participants. The rest of the nodes are hidden, and do not provide any information for topology discovery. We consider topology discovery under two routing models: (a) the participants exchange messages along the shortest paths and obtain end-to-end measurements, and (b) additionally, the participants exchange messages along the second shortest path. For scenario (a), our proposed algorithm results in a sub-linear edit-distance guarantee using a sub-linear number of uniformly selected participants. For scenario (b), we obtain a much stronger result, and show that we can achieve consistent reconstruction when a sub-linear number of uniformly selected nodes participate. This implies that accurate discovery of sparse random graphs is tractable using an extremely small number of participants. We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance. We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm even with a significant number of participants, and with the availability of end-to-end information along all the paths between the participants. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013 A recurrent challenge for modern applications is the processing of large graphs. The ability to generate representative samples of smaller size is useful not only to circumvent scalability issues but also, per se, for statistical analysis and other data mining tasks. For such purposes adequate sampling techniques must be devised. We are interested, in this paper, in the uniform random sampling of a connected subgraph from a graph. We require that the sample contains a prescribed number of vertices. The sampled graph is the corresponding induced graph. We devise, present and discuss several algorithms that leverage three different techniques: Rejection Sampling, Random Walk and Markov Chain Monte Carlo. We empirically evaluate and compare the performance of the algorithms. We show that they are effective and efficient but that there is a trade-off, which depends on the density of the graphs and the sample size. We propose one novel algorithm, which we call Neighbour Reservoir Sampling (NRS), that very successfully realizes the trade-off between effectiveness and efficiency.