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...ed in Section III-C3 has been recently compared with MHRW in the context of peer-to-peer sampling by Rasti et al. [17]. Further improvements or variants of random walks include random walk with jumps =-=[29,33]-=-, multiple dependent random walks [34], weighted random walks [35], or multigraph sampling [36]. Our work is most closely related to the random walk techniques. We obtain unbiased estimators of user p...

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...IS. This is the case in Fig. 4(d), where UIS is equivalent to WIS with w =1. Because no walk can mix faster than UIS (that is independent and thus has perfect mixing), improving the mixing time alone =-=[5,10,38,39]-=- cannot achieve the potential gains of stratification, in general. So far we focused on the smaller set Ctiny only. When estimating the size of Cbig, all errors are much smaller, but we observe simila...

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...ithm) through multiple dependent random walks [30], a random walk on a weighted graph (with a priori estimate of network information) [20], and the addition of random jumps (to anywhere in the graph) =-=[5]-=-. The corresponding Markov chains are time-reversible, whereas the main kernel of our proposed methods is transforming ‘any’ reversible Markov chain to its related non-reversible chain which avoids ba...

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...g techniques use variants of random walks (RW), such as the classic RW [20,27,41, 51,56], Metropolis-Hasting RW (MHRW) [18,20,42,51, 60], multiple dependent RW [52], multigraph RW [19], RW with jumps =-=[6,30,38,53]-=-, and weighted RW [35]. Based on the resulting (uniform or non-uniform) sample of nodes, there exist principled methods to estimate local graph properties (degree distribution, assortativity and clust...

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...T 0.7142 0.6741 5.6 CA-HEPPH 0.6004 0.7020 4.8 III. SAMPLING AND IDENTIFICATION METHODS A. Sampling Methods In this paper we consider six sampling methods (see Table II): 1) random-walk sampling (RW) =-=[8]-=-; 2) random-walk sampling with uniform restarts (RWJ and RWU) [8]; 3) frontier sampling (FS) [9]; 4) expansion sampling (XS) [10]; 5) adjusted expansion sampling (AXS); and 6) randomized expansion sam...

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...a random walk with uniform jumps which serves as a basic algorithm for quick detection of large degree nodes. The random walk with uniform jumps is described by the following transition probabilities =-=[1]-=- pij = { α/n+1 di+α α/n di+α , if i has a link to j, , if i does not have a link to j, (1) where di is the degree of node i. The random walk with uniform jumps can be regarded as a random walk on a mo...

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...trieval community has focussed on random walk based sampling algorithms like PageRank [33, 18]. There is also some work that highlights the different aspects of the sampling problem. Examples include =-=[19, 8, 5]-=- In social networks research, the recent work in [34] uses random walks to estimate node properties in G (e.g., degree distributions in online social networks). These different sampling algorithms foc...

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... The literature, however, provides some promising approaches to cope with this problem if the graph admits a limited (small) amount of RV sampling. RV sampling has been used to significantly reduce α =-=[1]-=- by allowing the random walks to “jump” to an RV sampled node. The algorithm in [1] differs from the PageRank [3] RW + RV “jumps” in that it obtains unbiased estimates of eq.(1). In [1] it is also sho...