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 lawsuits of the sixth foreign 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 provided have been conscientiously reviewed and chosen from various submissions for inclusion within the publication. The papers tackle a wide selection of issues relating to the learn of the Web-graph similar to theoretical and empirical research of the net graph and net 2.0 graphs, random walks on the net and net 2.0 graphs and their functions, and layout and function overview of the algorithms for social networks. The workshop papers were certainly clustered in 3 topical sections on graph versions for advanced networks, pagerank and net graph, and social networks and search.

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Extra info for Algorithms and Models for the Web-Graph: 6th International Workshop, WAW 2009, Barcelona, Spain, February 12-13, 2009. Proceedings

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Definition 3. We say an algorithm A(G, k) is a γ-approximation algorithm for the densest at-least-k-subgraph problem if, for any graph G and integer k, it returns an induced subgraph H ⊆ G with at least k vertices and density d(H) ≥ γDal (G, k). 3 Finding Dense Subgraphs with at Least k Vertices In this section, we describe an algorithm FindLargeDenseSubgraph that is a (1/3)-approximation algorithm for the densest at-least-k-subgraph problem and that runs in time O(m + n) in an unweighted graph.

Let Δ = maxv dv denote the maximum degree of G and δ = minv dv denote the minimum degree. For each vertex set S and a positive integer k, we define the k-th volume of G to be dkv . e. vol(G) = vol1 (G). We vol1 (G) define the average degree d = n1 vol(G) = vol and the second order average 0 (G) vol2 (G) ˜ degree d = . vol1 (G) Let D = diag(dv1 , dv2 , . . , dvn ) denote the diagonal degree matrix. Let 1 denote the column vector with all entries 1 and d = D1 be column vector of degrees. The normalized Laplacian of G is defined as 1 1 L = I − D− 2 AD− 2 .

The dense k-subgraph problem. Algorithmica 29(3), 410–421 (2001) 12. : On the densest k-subgraph problem, Technical report, Department of Applied Mathematics and Computer Science, The Weizmann Institute, Rehobot (1997) 13. : A fast parametric maximum flow algorithm and applications. SIAM J. Comput. 18(1), 30–55 (1989) 14. : Discovering large dense subgraphs in massive graphs. In: Proc. 31st VLDB Conference (2005) 15. : Finding a maximum density subgraph, Technical Report UCB/CSB 84/171, Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA (1984) 16.

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