By Béla Bollobás, Oliver Riordan (auth.), Stefano Leonardi (eds.)
This quantity comprises the 14 contributed papers and the contribution of the prestigious invited speaker B´ ela Bollob´ as awarded on the third Workshop on Algorithms and versions for the Web-Graph (WAW 2004), held in Rome, Italy, October sixteen, 2004, at the side of the forty fifth Annual IEEE Symposium on Foundations of machine technology (FOCS 2004). the realm huge internet has turn into a part of our way of life and knowledge retrievalanddataminingontheWebisnowofenormouspracticalinterest.Some of the algorithms assisting those actions are established considerably on viewing the net as a graph, triggered in numerous methods by way of hyperlinks between pages, hyperlinks between hosts, or different comparable networks. Theaimofthe2004WorkshoponAlgorithmsandModelsfortheWeb-Graph used to be to extra the knowledge of those Web-induced graphs, and stimulate the improvement of high-performance algorithms and functions that use the graphstructureoftheWeb.Theworkshopwasmeantbothtofosteranexchange of principles one of the varied set of researchers already excited by this subject, and to behave as an creation for the bigger group to the cutting-edge during this zone. This used to be the 3rd version of a really profitable workshop in this subject, WAW 2002 used to be held in Vancouver, Canada, along side the forty third - nual IEEE Symposium on Foundations of machine technological know-how, FOCS 2002, and WAW 2003 used to be held in Budapest, Hungary, together with the twelfth Int- nationwide world-wide-web convention, WWW 2003. This was once the ?rst variation of the workshop with formal proceedings.
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Extra info for Algorithms and Models for the Web-Graph: Third International Workshop, WAW 2004, Rome, Italy, October 16, 2004, Proceeedings
Let denote the set of ordered from E with distinct entries. Let B be the event that which occurs with probability by Lemma 3. We will now bound We will first determine E by revealing the sets Critically, Lemma 2 tells us that the potential edges in E are mutually independent and occur with the same probabilities as in G. Thus, Since Thus the probability that a given long edge survives is at most 30 R. Andersen et al. Proof of Theorem 8: Since there axe at most edges in G, with probability no long edges survive.
Rajagopalan, R. Stata, A. Tomkins, and J. Wiener, Graph structure in the web, Proc. of the 9th Intl. World Wide Web Conference (2002) 309–320. 13. G. Buckley and D. Osthus, Popularity based random graph models leading to a scale-free degree distribution, Discrete Mathematics 282 (2004) 53–68. 14. K. Chung, L. Lu, and V. Vu, Eigenvalues of random power law graphs, Annals of Combinatorics 7 (2003) 21–33. 15. K. Chung, L. Lu, and V. Vu, The spectra of random graphs with expected degrees, Proceedings of national Academy of Sciences 100 (2003) 6313–6318.
G. the size of the dominating set returned by a particular algorithm), the random process defined by setting and (for to be the expectation of Dominating Sets in Web Graphs 35 conditioned on the “exposure” of the first edges in the graph process is a martingale. t. the first edge exposures. In the forthcoming sections we will repeatedly use the following concentration result (for a proof see, for instance, ). Theorem 2. e. t. the presence of a single edge) and the ability to demonstrate the existence of a measure preserving bijection between in a same This is obvious in the random graph process as edges are inserted independently.