Concentration Inequalities and Martingale Inequalities: A Survey
Fan Chung,Lincoln Lu +1 more
TLDR
In this article, a number of generalized and extended versions of concentration inequalities and martingale inequalities are examined for analyzing processes with quite general conditions as illustrated in an example for an infinite Polya process and web graphs.Abstract:
We examine a number of generalized and extended versions of concentration inequalities and martingale inequalities. These inequalities are effective for analyzing processes with quite general conditions as illustrated in an example for an infinite Polya process and web graphs.read more
Citations
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Proceedings ArticleDOI
Random graphs
TL;DR: Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.
MonographDOI
Random Graphs and Complex Networks
TL;DR: This chapter explains why many real-world networks are small worlds and have large fluctuations in their degrees, and why Probability theory offers a highly effective way to deal with the complexity of networks, and leads us to consider random graphs.
Proceedings ArticleDOI
Influence Maximization in Near-Linear Time: A Martingale Approach
TL;DR: The proposed influence maximization algorithm is a set of estimation techniques based on martingales, a classic statistical tool that provides the same worst-case guarantees as the state of the art, but offers significantly improved empirical efficiency.
Posted Content
Stop-and-Stare: Optimal Sampling Algorithms for Viral Marketing in Billion-scale Networks
TL;DR: SSA and D-SSA as mentioned in this paper are two sampling frameworks for IM-based viral marketing problems, which are up to 1200 times faster than the SIGMOD'15 best method, IMM, while providing the same $(1-1/e-\epsilon) approximation guarantee.
ReportDOI
An Online Algorithm for Maximizing Submodular Functions
TL;DR: An algorithm for solving a broad class of online resource allocation problems, applied in environments where abstract jobs arrive one at a time, and one can complete the jobs by investing time in a number of abstract activities, according to some schedule.
References
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An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
Proceedings ArticleDOI
Random graphs
TL;DR: Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.