By Jeannette Janssen, Paweł Prałat, Rory Wilson (auth.), Anthony Bonato, Michael Mitzenmacher, Paweł Prałat (eds.)
This publication constitutes the refereed lawsuits of the tenth overseas Workshop on Algorithms and versions for the net Graph, WAW 2013, held in Cambridge, MA, united states, in December 2013. The 17 papers awarded have been conscientiously reviewed and chosen for inclusion during this quantity. They handle issues regarding graph-theoretic and algorithmic facets of comparable advanced networks, together with quotation networks, social networks, organic networks, molecular networks and different networks bobbing up from the Internet.
Read Online or Download Algorithms and Models for the Web Graph: 10th International Workshop, WAW 2013, Cambridge, MA, USA, December 14-15, 2013, Proceedings PDF
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Additional resources for Algorithms and Models for the Web Graph: 10th International Workshop, WAW 2013, Cambridge, MA, USA, December 14-15, 2013, Proceedings
The process proceeds in rounds. In each round, a node u that got infected in the previous round gets a chance to subsequently infect each healthy neighbor v, with probability equal to the weight of the edge (u, v), namely p(u, v). The node u becomes then recovered and does not spread the virus any further. If multiple nodes try to infect a new node in the current round, then each succeeds, independently, according to the corresponding edge weight. In this paper, we will focus on the the IC process only on undirected graphs.
A Local Clustering Algorithm for Connection Graphs 39 Now we will use this claim, the choice of α = φ2 /8γ, and the condition on the starting vertex q(k0 ) ≥ 1/γ vol(Sk0 ) to obtain a lower bound on q(kf ) , 4α φ2 vol(Sk0 ) 1 1 ≥ − γ vol(Sk0 ) 2γ vol(Sk0 ) 1 . 2, we have that p(C) ≥ 1 − 8γ , and therefore 1 ¯ p(C) ≤ 8γ . ¯ ¯ ≤ p(C) . This follows since q(kf ) vol(Sk ∩ Now observe that vol(Skf ∩ C) f q(kf ) ¯ ¯ C) = v∈Sk ∩C¯ q(kf ) dv ≤ v∈Sk ∩C¯ q(v) dv ≤ v∈C¯ p(v) = p(C). Thus f f ¯ p(C) q(kf ) 2γ vol(Skf ) ≤ 8γ 1 = vol(Skf ).
In this paper, we will focus on the the IC process only on undirected graphs. Throughout the text, we shall also refer to the stochastic infection strategy, as deﬁned by the IC process, as the oblivious stochastic strategy or sometime as the stochastic diﬀusion. Quantities of Interest. All graphs considered in the paper are undirected graphs. Throughout our analysis we will frequently refer to the minimum weighted cut value and maximum weighted cut value in the weighted input graph: the mini(resp.
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