By Andrei Broder (auth.), Ravi Kumar, Dandapani Sivakumar (eds.)
This publication constitutes the refereed complaints 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 overseas Workshop on web and community Economics (WINE 2010).
The thirteen revised complete papers and the invited paper offered have been rigorously reviewed and chosen from 19 submissions.
Read Online or Download Algorithms and Models for the Web-Graph: 7th International Workshop, WAW 2010, Stanford, CA, USA, December 13-14, 2010. Proceedings PDF
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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
LNCS, vol. 3595, pp. 710–716. Springer, Heidelberg (2005) 17. : Radius Plots for Mining Tera-byte Scale Graphs: Algorithms, Patterns, and Observations. In: SIAM Data Mining, SDM 2010 (2010) 18. : PEGASUS: A Peta-Scale Graph Mining System. In: IEEE Data Mining, ICDM 2009 (2009) 19. : Concentration of multivariate polynomials and its applications. Combinatorica 20(3), 417–434 (2000) 20. : Seminumerical Algorithms, 3rd edn. N. Kolountzakis et al. 21. 0468 22. : Main-memory triangle computations for very large (sparse (power-law)) graphs.
Hence, the right of the figure corresponds to maximizing the total number of vertices with positive holding power, while the left side corresponds to maximizing the sum of holding powers. The difference between the two is that the solutions on the right side may have a lot of nodes with barely positive values, while those on the left may have nodes further away from zero at the cost of more nodes with negative holding power. This is expected in general, but drastic change in the optimal solutions as we go from one extreme to another was surprising to us, and should be taken into account in further studies.
Hence the number of new alive nodes at time t is, conditional on the history Ht , a Binomial distributed random variable with parameters rt and Nt = n − t − Yt : Zt+1 |Ht ∼ Bin(Nt , rt ). (13) Now, by mathematical induction in t, it easily follows that for times t ≥ 1 the number of alive nodes Yt satisfies: t−1 Yt |Ht−1 ∼ Bin n − 1, 1 − (1 − rτ ) − t + 1. 2 Expectation and Variance of φt The history Ht embodies the evolution of how the attributes are discovered over time. It is insightful to recast that history in terms of the discovery times Γw of each attribute in W .