Algorithms and Models for the Web-Graph: 5th International by Abraham D. Flaxman, Juan Vera (auth.), Anthony Bonato, Fan

By Abraham D. Flaxman, Juan Vera (auth.), Anthony Bonato, Fan R. K. Chung (eds.)

This ebook constitutes the refereed court cases of the fifth foreign Workshop on Algorithms and types for the Web-Graph, WAW 2007, held in San Diego, CA, united states, in December 2007 - colocated with WINE 2007, the 3rd foreign Workshop on web and community Economics.

The thirteen revised complete papers and 5 revised brief papers provided have been rigorously reviewed and chosen from a wide pool of submissions for inclusion within the booklet. The papers handle a large choice of themes with regards to the research of the Web-graph corresponding to random graph versions for the Web-graph, PageRank research and computation, decentralized seek, neighborhood partitioning algorithms, and traceroute sampling.

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Additional info for Algorithms and Models for the Web-Graph: 5th International Workshop, WAW 2007, San Diego, CA, USA, December 11-12, 2007. Proceedings

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3 1 2 3 The density of a subgraph with k vertices is the fraction of the k(k − 1)/2 possible edges that exist in the subgraph. A more careful implementation, using a bucket-based priority queue, gives complexity O(n log n). , take a collection of m k-cliques and connect them via m additional edges. All nodes have a degree of k or k + 1 so the core is the whole graph. As m grows the density vanishes. Finding a Dense-Core in Jellyfish Graphs 31 Subramanian et al. [32] suggested a 5-tier hierarchical layering of the AS-graph.

Return C, H Our main result is the following: Theorem 2. Let G = (V, E) be a sparse graph that contains a (k, Ω(n1−β ), O(n1−β/2 ), c, )-Jellyfish subgraph. t. 5 For k = O(log n) and β ≤ 2/5, the time complexity of ˜ 1−β/2 )6 . Algorithm 2 is O(n The proof of Theorem 2 appears in the full version of the paper [20]. 5 Implementation To demonstrate the usefulness of our algorithms beyond their theoretical contribution, we conducted a performance evaluation of our algorithm in comparison with the GreedyMaxClique algorithm of Siganos et al.

Xt−1 .... 1 Introduction During the last decade a large body of research has centered on understanding and modeling the structure of large-scale networks like the Internet and the World Wide Web. Several recent books provide a general introduction to this topic [37] and [40]. , the proportion of vertices of degree at least k is proportional to k −α for some constant α). This has driven the investigation of random graph distributions which generate heavy-tailed degree distributions, including the fixed degree sequence model, the copying model, and the preferential attachment model.

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