By Abraham D. Flaxman, Juan Vera (auth.), Anthony Bonato, Fan R. K. Chung (eds.)
This booklet constitutes the refereed lawsuits of the fifth overseas 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 overseas Workshop on web and community Economics.
The thirteen revised complete papers and 5 revised brief papers awarded have been rigorously reviewed and chosen from a wide pool of submissions for inclusion within the e-book. The papers deal with a wide selection of subject matters regarding the examine of the Web-graph corresponding to random graph types 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
Avrachenkov, N. S. Pham PageRank Mass of ESCC Let us now consider the PageRank mass of the Extended SCC component (ESCC) described in Section 3, as a function of c ∈ [0, 1]. Subdividing the PageRank vector in the blocks π = [πPureOUT πESCC ], from (5) we obtain ||πESCC (c)|| = (1 − c)γuESCC [I − cT ]−1 1, (16) where T represents the transition probabilitites inside the ESCC block, γ = |ESCC|/n, and uESCC is a uniform probability row-vector over ESCC. Clearly, we have ||πESCC (0)|| = γ and ||πESCC (1)|| = 0.
Organization: In Section 2 we give definitions and notations. In Section 3 we describe and analyze a simple randomized algorithm (JellyCore) for finding the densecore, which serves as a basis for our sublinear algorithm. In Section 4 we modify the JellyCore algorithm to a sublinear algorithm. In Section 5 we give an implementation of the JellyCore algorithm and compare it to the algorithms of Carmi et al.  and Siganos et al. . We summarize our conclusions in Section 6. , |E| = O(n), where n = |V |.
5. Return C, H Our main result is the following: Theorem 1. Let G = (V, E) be a sparse graph that contains a (k, d, c, )-Jellyfish subgraph. t. |H| ≤ (1 + )|H|. The time complexity of Algorithm 1 is O(n log n). Intuitively, the algorithm works in graphs that contain (k, d, c, )-Jellyfish subgraphs since in such graphs it suffices to sample a small set of vertices and observe their neighbors. The set of the neighbors with degree at least d is close to a nucleus H. In addition, in graphs that contain (k, d, c, )-Jellyfish subgraphs each vertex in C neighbors most of the vertices in H, and there might be only few vertices outside C that neighbor most of the vertices in H.
Algorithms and Models for the Web-Graph: 5th International Workshop, WAW 2007, San Diego, CA, USA, December 11-12, 2007. Proceedings by Abraham D. Flaxman, Juan Vera (auth.), Anthony Bonato, Fan R. K. Chung (eds.)