Random Walks with Look-Ahead in Scale-Free Random Graphs

Cooper, Colin; Frieze, Alan

doi:10.1137/090762178

Cited by 3 publications

(6 citation statements)

References 12 publications

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“…Random walks with lookahead have been the subject of a number of works. Cooper and Frieze [8] studied the cover time of RW. Mihail et al [31] shows that a RW with one-hop lookahead finds the majority of nodes in sublinear time in an infinite configuration model with heavy tailed power law degree distribution.…”

Section: Related Workmentioning

confidence: 99%

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Pay few, influence most: Online myopic network covering

Avrachenkov¹,

Basu²,

Neglia³

et al. 2014

2014 IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS)

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Efficient marketing or awareness-raising campaigns seek to recruit n influential individuals -where n is the campaign budget -that are able to cover a large target audience through their social connections. So far most of the related literature on maximizing this network cover assumes that the social network topology is known. Even in such a case the optimal solution is NP-hard. In practice, however, the network topology is generally unknown and needs to be discovered on-the-fly. In this work we consider an unknown topology where recruited individuals disclose their social connections (a feature known as one-hop lookahead). The goal of this work is to provide an efficient greedy online algorithm that recruits individuals as to maximize the size of target audience covered by the campaign.We propose a new greedy online algorithm, Maximum Expected d-Excess Degree (MEED), and provide, to the best of our knowledge, the first detailed theoretical analysis of the cover size of a variety of well known network sampling algorithms on finite networks. Our proposed algorithm greedily maximizes the expected size of the cover. For a class of random power law networks we show that MEED simplifies into a straightforward procedure, which we denote MOD (Maximum Observed Degree). We substantiate our analytical results with extensive simulations and show that MOD significantly outperforms all analyzed myopic algorithms. We note that performance may be further improved if the node degree distribution is known or can be estimated online during the campaign.

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Section: Related Workmentioning

confidence: 99%

“…Let us consider the following perturbation equation with ε as some scaling parameter. Equating terms in (8) with ε 0 , we obtain…”

Section: Appendix a Rw And Independent Edge Sampling Approximationmentioning

confidence: 99%

Pay few, influence most: Online myopic network covering

Avrachenkov¹,

Basu²,

Neglia³

et al. 2014

2014 IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS)

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“…Note that R [3] only has 4 elements while there are 7 one-way paths with length 3. This is the effect of combining redundant paths by summarizing one-way paths.…”

Section: Definition 4 (Summation Of One Way Pathsmentioning

confidence: 99%

“…However, many real-world graphs are scalefree [3] which means there is a small portion of high-degree nodes. These nodes pose a significant challenge to the SimRankbased similarity join problem, because if the path tree generated by Algorithm 1 contains such nodes, it will spread a lot of branches and reduce the efficiency.…”

Section: Approximation Algorithm For Scale-free Graphsmentioning

confidence: 99%

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Efficient top-k simrank-based similarity join

Tao

2014

Proc. VLDB Endow.

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SimRank is a popular and widely-adopted similarity measure to evaluate the similarity between nodes in a graph. It is time and space consuming to compute the SimRank similarities for all pairs of nodes, especially for large graphs. In real-world applications, users are only interested in the most similar pairs. To address this problem, in this paper we study the top-k SimRank-based similarity join problem, which finds k most similar pairs of nodes with the largest SimRank similarities among all possible pairs. To the best of our knowledge, this is the first attempt to address this problem. We encode each node as a vector by summarizing its neighbors and transform the calculation of the SimRank similarity between two nodes to computing the dot product between the corresponding vectors. We devise an efficient two-step framework to compute top-k similar pairs using the vectors. For large graphs, exact algorithms cannot meet the high-performance requirement, and we also devise an approximate algorithm which can efficiently identify topk similar pairs under user-specified accuracy requirement. Experiments on both real and synthetic datasets show our method achieves high performance and good scalability.

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Inequalities on partial correlations in Gaussian graphical models containing star shapes

Jones

Didelez²

2016

Communications in Statistics - Theory and Methods

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This short paper proves inequalities that restrict the magnitudes of the partial correlations in star-shaped structures in Gaussian graphical models. These inequalities have to be satisfied by distributions that are used for generating simulated data to test structure-learning algorithms, but methods that have been used to create such distributions do not always ensure that they are. The inequalities are also noteworthy because stars are common and meaningful in real-world networks.

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Random Walks with Look-Ahead in Scale-Free Random Graphs

Abstract: If m ≥ 2 is constant and 0 ≤ r ≤ ε log log n for a small positive constant ε, then whp a random walk with look-ahead r on a scale-free graph G = G ( m, n) has cover time C G (r) ∼ (2/(m r−1 (m − 1))) n log n.

Cited by 3 publications

References 12 publications

Pay few, influence most: Online myopic network covering

Pay few, influence most: Online myopic network covering

Efficient top-k simrank-based similarity join

Inequalities on partial correlations in Gaussian graphical models containing star shapes

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