Download Algorithms and Models for the Web-Graph: 6th International by Kevin J. Lang (auth.), Konstantin Avrachenkov, Debora PDF

By Kevin J. Lang (auth.), Konstantin Avrachenkov, Debora Donato, Nelly Litvak (eds.)

This e-book constitutes the refereed lawsuits of the sixth overseas Workshop on Algorithms and versions for the Web-Graph, WAW 2009, held in Barcelona, Spain, in February 2009 - co-located with WSDM 2009, the second one ACM overseas convention on internet seek and information Mining.

The 14 revised complete papers awarded have been conscientiously reviewed and chosen from various submissions for inclusion within the e-book. The papers tackle a large choice of themes on the topic of the research of the Web-graph reminiscent of theoretical and empirical research of the net graph and net 2.0 graphs, random walks on the net and internet 2.0 graphs and their purposes, and layout and function overview of the algorithms for social networks. The workshop papers were evidently clustered in 3 topical sections on graph types for advanced 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

Example text

Take an initial set S0 max(Cσ 2 vol(G), Δ ln n) ≤ vol(S0 ) ≤ max(Cσ 2 vol(G), Δ ln n) + Δ. Let T0 = U ′ \ S0 . For i ≥ 1, we will recursively define Si = Γ Gp (Si−1 )∩U ′ and 2 (Ti )vol(G) . Ti = U ′ \ ∪ij=0 Sj until vol2 (Ti ) ≤ (1 − 3ǫ)vol2 (G) or vol(Si ) ≥ 2δvol 5pvol3 (Ti ) Condition 1 in Lemma 3 is always satisfied. 5p 2 5(1 + c) 2 2 σΔ 2 5(1 + c) σ max d2v vol(G) ≤ vol2 (G) ) σ Δ vol(G) = ( ˜ 2δ v∈Ti 2δ 2dδ d˜ = o(vol2 (G)) ≤ vol2 (Ti ). Condition 3 in Lemma 3 is also trivial because δ 2 vol2 (Ti )2 δ 2 vol2 (Ti )2 δ 2 (1 − 3ǫ)vol2 (G) ≥ ≥ 2 2 2 2 2 25p σ vol5 (Ti ) 25p σ Δ vol3 (Ti ) 25p2 σ 2 Δ2 M d d˜ 2 δ 2 (1 − 3ǫ) ) vol(G) = ω(vol(G)).

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. Taking w = αd = αW/n, we learn that W (Cαd (G)) > (1 − α)W . ⊓ ⊔ Proof (Theorem 1). Let {H1 , . . , Hn } be the induced subgraphs computed by FindLargeDenseSubgraph on the input graph G. It suffices to show that for any k, there is an integer I ∈ [k, n] satisfying d(HI ) ≥ Dal (G, k)/3.

Polynomial time approximation schemes for dense instances of NP-hard problems. In: Proc. 27th ACM Symposium on Theory of Computing (STOC 1995), pp. 284–293 (1995) 5. : Complexity of finding dense subgraphs. Discrete Appl. Math. 121(1-3), 15–26 (2002) 6. : Greedily finding a dense subgraph. J. Algorithms 34(2), 203–221 (2000) 7. : Greedy approximation algorithms for finding dense components in a graph. , Khuller, S. ) APPROX 2000. LNCS, vol. 1913, pp. 84–95. Springer, Heidelberg (2000) 8. : A scalable pattern mining approach to web graph compression with communities.

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