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 versions for the Web-Graph, WAW 2012, held in Halifax, Nova Scotia, Canada, in June 2012. The thirteen papers offered have been rigorously reviewed and chosen for inclusion during this quantity. They tackle a few subject matters relating to the complicated networks such hypergraph coloring video games and voter types; algorithms for detecting nodes with huge levels; random Appolonian networks; and a sublinear set of rules for Pagerank computations.

**Read 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**

**Example text**

I=1 1 . ti 36 C. Cooper, A. Frieze, and P. Pralat Let k ∗ = C log t, where C = 18 max(1, A2 ). Assuming t suﬃciently large, and recalling that pA1 < 1, we have EN (v, u, k) ≤ 2A2 k>k∗ k>k∗ ≤ 2A2 (1 + o(1))A2 pe(log v/u + 1/u) k−1 (1 + o(1))A2 e(log v/u + 1/u) C log t k∗ k−1 1 1 − 3A2 /C = O(6−18 log t ) = o(t−4 ). The result follows for u tending to inﬁnity. In the case where u is a constant, it follows from Theorem 1 that a multiplicative correction of e can be used in E(deg− (ti−1 , ti )), leading to an error term of O(t−18 log 2 ) = o(t−4 ), as before.

D(Gt ) = O(log t). In fact, we conjecture that this result is best possible; that is, the following holds: Conjecture 1. s. D(Gt ) = Θ(log t). We will try to settle this down in the journal version of this paper. 2. 1 35 Upper Bound An O(log t) upper bound on the directed diameter is obtained as follows. Theorem 5. Let C = 18 max(A2 , 1). With probability 1 − o(t−2 ) we have that for any 1 ≤ i < j ≤ t, Gt does not contain a directed (vi , vj )-path of length at least k ∗ = C log t. As there are at most t2 pairs vi , vj , the Theorem 4 will follow as well.

Some Typical Properties of the Spatial Preferred Attachment Model 37 Let us recall that Vt ⊆ S where S is the unit hypercube [0, 1]m . We use the geometry of the model to obtain a sparse cut. Let S = s = (s1 , s2 , . . , sm ) ∈ S : s1 < 1 2 . Let us partition the vertex set Vt as follows: Vt = Vt ∩ S , Vt = Vt ∩ (S \ S ) = Vt \ Vt . The next theorem shows that this partition yields a sparse cut. Theorem 6. s. the following holds |Vt | = (1+o(1))t/2, |Vt | = (1+o(1))t/2, and |E(Vt , Vt )| = O(tmax{1−1/m,pA1 } log5 t) = o(t).