By Abraham D. Flaxman, Juan Vera (auth.), Anthony Bonato, Fan R. K. Chung (eds.)
This publication constitutes the refereed complaints of the fifth foreign Workshop on Algorithms and versions for the Web-Graph, WAW 2007, held in San Diego, CA, united states, in December 2007 - colocated with WINE 2007, the 3rd overseas Workshop on net and community Economics.
The thirteen revised complete papers and 5 revised brief papers offered have been conscientiously reviewed and chosen from a wide pool of submissions for inclusion within the booklet. The papers handle a large choice of themes relating to the examine of the Web-graph resembling random graph versions for the Web-graph, PageRank research and computation, decentralized seek, neighborhood partitioning algorithms, and traceroute sampling.
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Extra info for Algorithms and Models for the Web-Graph: 5th International Workshop, WAW 2007, San Diego, CA, USA, December 11-12, 2007. Proceedings
Large scale networks fingerprinting and visualization using the k-core decomposition. Proc. Neural Information Processing Systems (August 2005) 3. : Greedily finding a dense subgraph. Journal of Algorithms 34, 203–221 (2000) 4. : An incremental super-linear preferential Internet topology model. , Pratt, I. ) PAM 2004. LNCS, vol. 3015, pp. 53–62. Springer, Heidelberg (2004) 5. : A geographic directed preferential Internet topology model. Computer Networks 51(14), 4174–4188 (2007) 6. : On the marginal utility of network topology measurements.
F = F2 : I = Θ(1) and we can take ρ = 1, μ = Ω(1), c3 = Ω(1). We have a problem ﬁtting the case of F1 with β = 2 into the theorem. We now consider conditons under which Gn is an expander. Let F be tame if there exist absolute constants C1 , C2 such that (T1) F (x) ≥ C1 for 0 < x ≤ π. (T2) I ≤ C2 . We note that F1 with β < 2 is tame since F1 (x) ≥ π −β for 0 ≤ π and I= 1 2 π x−β sin xdx ≤ x=0 π 2−β . 2(2 − β) The conductance Φ of Gn is deﬁned by Φ= min degn (K)≤mn Φ(K) = ¯ |E(K : K)| . degn (K)≤mn degn (K) min Theorem 3.
Remark 1. Note that the exponent in (a) does not depend on the particular function F . F manifests itself only through the error terms. For Part (a) of the above theorem: F F F F F = F0 : θ = 0. = F1 , β > 2: θ = 2δ. = F1 , β < 2: θ = 0. = F1 , β = 2: θ = 2δ. = F2 : θ = 0. For Part (b) of the above theorem: F = F0 : η = r, ϕ = 0. F = F1 , β > 2: η = n−δ , ϕ = O(n−(β−2)δ ). F = F1 , β = 2: η = lnlnlnnn , ϕ = O(η). We now consider the connectivity and diameter of Gn . For this we will place some more restrictions on F .