Continuum Percolation with Unreliable and Spread-Out Connections |
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Authors: | Massimo Franceschetti Lorna Booth Matthew Cook Ronald Meester Jehoshua Bruck |
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Institution: | (1) Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, 9500 Gilman Drive, Mail Code 0407, CA 92093-0407, USA;(2) Department of Computation and Neural Systems, Caltech, MC 136-93 Pasadena, CA 91125, USA;(3) Division of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands;(4) Department of EECS, UC, Berkeley, CA, 94720-1770 |
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Abstract: | We derive percolation results in the continuum plane that lead to what appears to be a general tendency of many stochastic network models. Namely, when the selection mechanism according to which nodes are connected to each other, is sufficiently spread out, then a lower density of nodes, or on average fewer connections per node, are sufficient to obtain an unbounded connected component. We look at two different transformations that spread-out connections and decrease the critical percolation density while preserving the average node degree. Our results indicate that real networks can exploit the presence of spread-out and unreliable connections to achieve connectivity more easily, provided they can maintain the average number of functioningconnections per node. |
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Keywords: | Continuum percolation random connection model Poisson processes stochastic networks unreliable connections |
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