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

ISBN-10: 3540770038

ISBN-13: 9783540770039

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.

**Read or Download Algorithms and Models for the Web-Graph: 5th International Workshop, WAW 2007, San Diego, CA, USA, December 11-12, 2007. Proceedings PDF**

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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**

**Example text**

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. [10] and Siganos et al. [31]. 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.)

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