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

ISBN-10: 3540770038

ISBN-13: 9783540770039

This ebook constitutes the refereed complaints 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 foreign Workshop on net 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 e-book. The papers tackle a large choice of issues regarding the learn of the Web-graph reminiscent of random graph types for the Web-graph, PageRank research and computation, decentralized seek, neighborhood partitioning algorithms, and traceroute sampling.

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

**Sample text**

The JellyCore algorithm for approximating C and H) 1. Uniformly and independently at random select s vertices. Let S be the set of vertices selected. 2. Compute H = {v ∈ Γ (S) | deg(v) ≥ d}. If H = ∅ then abort. 3. Compute the set Γ2 (H) of vertices that neighbor all but at most of 2 |H| vertices in H. 4. Order the vertices in Γ2 (H) according to their degree in the subgraph induced by Γ2 (H) (breaking ties arbitrarily). Let C be the first k vertices according to this order. 5. Return C, H Our main result is the following: Theorem 1.

A Geometric Preferential Attachment Model of Networks II 43 – Time step 0: To initialize the process, we start with G0 being the Empty Graph. – Time step t + 1: We choose vertex xt+1 uniformly at random in S and add it to Gt . Let T (xt+1 ) = F (|xt+1 − v|) degt (v). v∈Vt We add m random edges (xt+1 , yi ), i = 1, 2, . . , m incident with xt+1 . Here, each yi is chosen independently from Vt+1 = Vt ∪ {xt+1 } (parallel edges and loops are permitted), such that for each i = 1, . . ) Pr(yi = xt+1 ) = 1 − For z > 0 we deﬁne Iz = 1 2 z F (x) sin x dx and Jz = I − Iz .

Right: Core Density. almost identical, particularly for n ≥ 18, 000 vertices. The density of GreedyMaxClique is obviously 1, by the algorithm definition. We can conclude that the practical results of the JellyCore algorithm, on the real AS graph, agree extremely well with the results of both kCore and GreedyMaxClique. 12000 Execution time [mSec] 10000 kCore JellyCore GreedyMaxClique 8000 6000 4000 2000 0 11,000 13,000 15,000 17,000 Number of vertices 19,000 21,000 Fig. 3. 2 Execution Times Figure 3 shows that the running times of JellyCore and GreedyMaxClique are almost identical, and that kCore is indeed slower: Jellycore runs about 6 times faster than kCore on the largest AS graphs.

### 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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