Algorithms and Models for the Web-Graph: 6th International by Kevin J. Lang (auth.), Konstantin Avrachenkov, Debora

By Kevin J. Lang (auth.), Konstantin Avrachenkov, Debora Donato, Nelly Litvak (eds.)

This ebook constitutes the refereed complaints of the sixth overseas Workshop on Algorithms and types for the Web-Graph, WAW 2009, held in Barcelona, Spain, in February 2009 - co-located with WSDM 2009, the second one ACM foreign convention on net seek and information Mining.

The 14 revised complete papers offered have been rigorously reviewed and chosen from various submissions for inclusion within the e-book. The papers deal with a wide selection of themes regarding the examine of the Web-graph equivalent to theoretical and empirical research of the internet graph and net 2.0 graphs, random walks on the internet and internet 2.0 graphs and their purposes, and layout and function review of the algorithms for social networks. The workshop papers were clearly clustered in 3 topical sections on graph types for advanced networks, pagerank and net graph, and social networks and search.

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Example text

For all u ∈ N (v) T RGv (u)= result of Algorithm 2 (Gv ,u, k = 3, ǫ, δ). T LG(v) = T LG(v) + u∈N (v) T RGv (u). av = 0. For all u ∈ N (v) go over v’s adjacency list, and for each vertex w in u’s adjacency list check if w ∈ N (v) by going over v’s adjacency list. If w ∈ N (v) then av = av + deg w − 2 + deg u − 2. Return T LG(v) + av . Theorem 4. Let G = (V, E) be an undirected graph, and let H be a triangle with a ”tail” of length one. Then, for every vertex v, the number of copies of G that are isomorphic to H and adjacent to v can be (ǫ, δ)-approximated, with time complexity O |E|2 + n · |E| log(1/δ)/ǫ2 .

In this case, we say that f and g are of the same order. Also, f (n) = ω(g(n)) if g(n) = o(f (n)). We note that under the assumption that the maximum degree Δ of G satis˜ fying Δ = o( σd ), it can be shown that the spectral norm of the adjacency matrix ˜ Under the assumption in Theorem 2, we observe satisfies A = ρ = (1 + o(1))d. that the percolation threshold of G is d1˜. To examine when the conditions of Theorems 1 and 2 are satisfied, we note that admissibility implies that d˜ = Θ(d), which essentially says that while there can be some vertices with degree much higher than d, there cannot be too many.

We refer to these as the densest atleast-k-subgraph problem (dalks), and the densest at-most-k-subgraph problem (damks). These two relaxed versions of the densest k-subgraph problem roughly correspond to the two types of applications for dense subgraphs described earlier; for finding communities one would want an algorithm to solve damks, and for preprocessing a graph one would want an algorithm for dalks. Our main result is to show that dalks can be solved efficiently, while damks is nearly as hard to approximate as dks.

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Algorithms and Models for the Web-Graph: 6th International by Kevin J. Lang (auth.), Konstantin Avrachenkov, Debora
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