Algorithms and Models for the Web Graph: 9th International by Fan Chung, Alexander Tsiatas (auth.), Anthony Bonato,

By Fan Chung, Alexander Tsiatas (auth.), Anthony Bonato, Jeannette Janssen (eds.)

This ebook constitutes the refereed complaints of the ninth foreign Workshop on Algorithms and types for the Web-Graph, WAW 2012, held in Halifax, Nova Scotia, Canada, in June 2012. The thirteen papers provided have been conscientiously reviewed and chosen for inclusion during this quantity. They handle a couple of issues regarding the advanced networks such hypergraph coloring video games and voter versions; algorithms for detecting nodes with huge levels; random Appolonian networks; and a sublinear set of rules for Pagerank computations.

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Example text

Fix 0 ≤ k < log t, and let vi ∈ V (k) . Note that the maximum radius of influence of vi is O((e−k log2 t)1/m ). Therefore, if there is an edge in the cut directed to vi = (s1 , s2 , . . , sm ), then vi must fall into a strip within distance O((e−k log2 t)1/m ) from the cutting hyperplane; that is, |s1 − 1/2| = O((e−k log2 t)1/m ). Since |V (k) | = O(ek ), we get that O((e−k log2 t)1/m ) · |V (k) | = O(ek(1−1/m) (log t)2/m ) vertices of V (k) are expected to appear in this strip during the whole process.

Therefore, if p > p1 := (A1 + A2 )−1 , then the process is deg+ (vt , t) = 1−pA 1 expected out degree in Gt is larger than 1, and so is the expected degree in ˆ t . s. there exists a giant component if p > p1 . On the other hand, if p < p1 , then the expected out-degree in Gt is smaller than one, but ˆ t . Is p1 this fact does not in itself guarantee absence of the giant component in G + −1 the threshold we search for? If p < p2 := (A1 + 2A2 ) , then deg (vt , t) < 1/2 ˆ t is smaller than one. Perhaps p2 is the threshold and so the average degree in G for the giant component?

K p Pr(vP u) = i=1 A1 deg− (ti−1 , ti ) + A2 ti . Let N (v, u, k) be the number of directed (v, u)-paths of length k, then k pk E EN (v, u, k) = u

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