Algorithms and Models for the Web-Graph: 7th International by Ravi Kumar, D Sivakumar

By Ravi Kumar, D Sivakumar

This booklet constitutes the refereed lawsuits of the seventh foreign Workshop on Algorithms and types for the Web-Graph, WAW 2010, held in Stanford, CA, united states, in December 2010, which was once co-located with the sixth foreign Workshop on net and community Economics (WINE 2010). The thirteen revised complete papers and the invited paper awarded have been rigorously reviewed and chosen from 19 submissions.

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Additional info for Algorithms and Models for the Web-Graph: 7th International Workshop, WAW 2010, Stanford, CA, USA, December 13-14, 2010, Proceedings (Lecture Notes in Computer Science)

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RIGs can be interpreted as a model for large randomly formed non-metric data sets. We analyze the component evolution in general RIGs, giving conditions on the existence and uniqueness of the giant component. Our techniques generalize existing methods for analysis of component evolution: we analyze survival and extinction properties of a dependent, inhomogeneous Galton-Watson branching process on general RIGs. Our analysis relies on bounding the branching processes and inherits the fundamental concepts of the study of component evolution in Erd˝os-R´enyi graphs.

Suppose that pw = O(1/n) for all w p3w = O(1/n2 ). and w∈W For any positive constant c < 1, if w∈W p2w = c/n, then whp2 all components in a general random intersection graph G(n, m, p) are of order O(log n). Proof. We generalize the techniques used in the proof for the sub-critical case in Gn,p presented in [2]. Let T (v0 ) be the stopping time defined in (9), for the process starting d at node v0 and recall that T (v0 ) = |C(v0 )|. We will bound the size of the largest component, and prove that under the conditions of the theorem, all components are of order O(log n), whp.

Inf. Sci. 23(4), 661–674 (2009) 9. : The representation of a graph by set intersections. Canad. J. Math. 18, 106–112 (1966) 10. : Random intersection graphs and classification. In: Advances in Data Analysis, vol. 45, pp. 67–74 (2007) 11. : Modelling disease outbreaks in realistic urban social networks. Nature 429(6988), 180– 184 (2004) 12. : Random intersection graphs when m = ω(n): An equivalence theorem relating the evolution of the g(n, m, p) and g(n, p) models. Random Struct. Algorithms 16(2), 156–176 (2000) 13.

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