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.
Read Online or Download Algorithms and Models for the Web Graph: 9th International Workshop, WAW 2012, Halifax, NS, Canada, June 22-23, 2012. Proceedings PDF
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Additional info for Algorithms and Models for the Web Graph: 9th International Workshop, WAW 2012, Halifax, NS, Canada, June 22-23, 2012. Proceedings
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