Download e-book for kindle: 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 overseas 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 awarded have been rigorously reviewed and chosen from a number of submissions for inclusion within the e-book. The papers handle a large choice of themes with regards to the research of the Web-graph comparable to theoretical and empirical research of the internet graph and net 2.0 graphs, random walks on the internet and internet 2.0 graphs and their purposes, and layout and function assessment of the algorithms for social networks. The workshop papers were clearly clustered in 3 topical sections on graph types for complicated networks, pagerank and internet graph, and social networks and search.

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

Sample text

It is an interesting open question to describe the precise scaling window for percolation for the more general graphs studied here. ) Compared with earlier results, the main advantage of our results is the ability to handle general degree sequences. To state our results, we give a few definitions here. For a subset S of vertices, the volume of S, denoted by vol(S) is the sum of degrees of vertices in S. e. volk (S) = v∈S dkv . We write vol1 (S) = vol(S) and volk (G) = volk (V (G)), where V (G) is the vertex set of G.

Arora, Karger, and Karpinski [4] gave a PTAS for the special case k = Ω(n) and m = Ω(n2 ). Asahiro, Hassin, and Iwama [5] showed that the problem is still N P-complete for very sparse graphs. Kannan and Vinay [16] introduced a different objective function for density, which is defined for a pair of vertex subsets S and T rather than a single subgraph. They gave an O(log n)-approximation for this objective function using spectral techniques. Charikar [7] later gave a linear time (1/2)-approximation algorithm for this objective function, based on the core decomposition, and showed that the problem can be solved exactly by linear programming.

Proof. Let {H1 , . . , Hn } be the induced subgraphs determined by FindLargeDenseSubgraph on the input graph G. Fix a value of w, and let I(w) be the largest index such that rI(w) ≥ w. Recall that HI(w) = Cw (G) by Lemma 1. Since each edge in G is removed once during the course of the algorithm, n W = ri i=1 I(w) n ri ri + = i=1 i=I(w)+1 < W (HI(w) ) + w · (n − I(w)) ≤ W (Cw (G)) + w · n. Therefore, W (Cw (G)) > W − w · n. Taking w = d = W/n in the equation above, we learn that W (Cd (G)) > 0.

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