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

This e-book constitutes the refereed lawsuits of the ninth overseas 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 rigorously reviewed and chosen for inclusion during this quantity. They handle a couple of issues concerning the advanced 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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**Extra info for Algorithms and Models for the Web Graph: 9th International Workshop, WAW 2012, Halifax, NS, Canada, June 22-23, 2012. Proceedings**

**Example text**

The directed diameter of a graph Gt is deﬁned as D(Gt ) = max l(vi , vj ). 1) is devoted to proving the following result: Theorem 4. s. 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.

Proof. Clearly, we expect t/2 vertices in each set Vt and Vt . The concentration follows immediately from Chernoﬀ bound. s. s. for every i ∈ [t] the maximum sphere of inﬂuence of a vertex vi added at time i is O(i−1 log2 t) (during the whole process). , we may assume that this property holds for all i. Therefore, the maximum radius of inﬂuence of vi is O((log 2 t/i)1/m ). We will investigate how many edges are in the cut by counting (independently) edges in this cut directed to vertices of similar age.

On Communication, Control, and Computing, pp. 182–191 (2001) 28. : A mathematical theory of evolution based on the conclusions of Dr. C. Willis. Philosophical Transactions of the Royal Society of London (Series B) 213, 21–87 (1924) 29. : Collective dynamics of ‘small-world’ networks. edu Abstract. In a network, identifying all vertices whose PageRank is more than a given threshold value Δ is a basic problem that has arisen in Web and social network analyses. In this paper, we develop a nearly optimal, sublinear time, randomized algorithm for a close variant of this problem.