By Jeannette Janssen, Paweł Prałat, Rory Wilson (auth.), Anthony Bonato, Michael Mitzenmacher, Paweł Prałat (eds.)

This e-book constitutes the refereed lawsuits of the tenth foreign Workshop on Algorithms and versions for the internet Graph, WAW 2013, held in Cambridge, MA, united states, in December 2013. The 17 papers provided have been rigorously reviewed and chosen for inclusion during this quantity. They deal with subject matters on the topic of graph-theoretic and algorithmic elements of similar complicated 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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**Extra resources for Algorithms and Models for the Web Graph: 10th International Workshop, WAW 2013, Cambridge, MA, USA, December 14-15, 2013, Proceedings**

**Sample text**

WAW 2007. LNCS, vol. 4863, pp. 41–55. Springer, Heidelberg (2007) 14. : Spatial preferential attachment networks: Power laws and clustering coeﬃcients. 3830 (2012) 15. : Geometric graph properties of the spatial preferred attachment model. Adv. Appl. Math. 50, 243–267 (2013) 16. : Degree sequences of geometric preferential attachment graphs. Adv. in Appl. Probab. 42, 319–330 (2010) 17. : Continuum percolation. Cambridge Tracts in Mathematics, vol. 119. Cambridge University Press, Cambridge (1996) 18.

In this work, we initiate the study of adversarial infection strategies which can decide intelligently which neighbors of infected nodes to infect next in order to maximize their spread, while maintaining a similar “signature” as the oblivious stochastic infection strategy as not to be discovered. We ﬁrst establish that computing an optimal and near-optimal adversarial strategies is computationally hard. We then identify necessary and suﬃcient conditions in terms of network structure and edge infection probabilities such that the adversarial process can infect polynomially more nodes than the stochastic process while maintaining a similar “signature” as the oblivious stochastic infection strategy.

Let kf be the ﬁnal vertex considered by the algorithm. Claim. , kf is a sequence of vertices satisfying both 2α – q(vki+1 ) ≥ q(vki ) − φ vol(S ki ) – vol(Ski+1 ) ≥ (1 + φ) vol(Ski ) then q(kf ) ≥ q(k0 ) − 4α . φ2 vol(Sk0 ) Proof. We note that vol(Ski+1 ) ≥ (1 + φ)i vol(Sk0 ), and so we have q(kf ) ≥ q(k0 ) − 2α 2α 2α − − ··· − φ vol(Sk0 ) φ vol(Sk1 ) φ vol(Skf −1 ) 1 2α 1 + ···+ 1+ φ vol(Sk0 ) 1+φ (1 + φ)f −1 2α 1+φ ≥ q(k0 ) − φ vol(Sk0 ) φ 4α ≥ q(k0 ) − 2 φ vol(Sk0 ) ≥ q(k0 ) − and the claim follows.