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SUMMARY:Optimal flows on random graphs - van der Hofstad\, R (TU Eindhoven
 )
DTSTART:20130815T090000Z
DTEND:20130815T094500Z
UID:TALK46655@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We investigate minimal-weight problems on the configuration mo
 del\, in which flow passes through the network minimizing the total weight
  along edges. In practice\, one is both interested in the actual weight of
  the minimal weight path\, which represents its cost\, as well as the numb
 er of edges used or hopcount\, as this is often a good measure of the dela
 y observed in the network. \n\nWe assume that the edge weights are indepen
 dent continuous random variables\, leading to first passage percolation on
  the configuration model. We then investigate the total weight and hopcoun
 t of the minimal weight path. We study how the minimal weight and hopcount
  depend on the structure of the edge weights as well as on the structure o
 f the graph. Our proofs crucially rely on the connection between first pas
 sage percolation and continuous-time branching processes\, which is due to
  the tree-like nature of the configuration model.\n\nThe above research is
  inspired by transport in real-world networks\, such as the Internet. Meas
 urements have shown fascinating features of the Internet\, such as the `sm
 all world phenomenon'. The small-world phenomenon states that typical dist
 ances in the network under consideration is small. Also\, the degrees in t
 he Internet are rather different from the degree structure in classical ra
 ndom graphs. Internet is a key example of a complex network\, other exampl
 es being the Internet Movie Data Base\, social networks\, biological netwo
 rks\, the WWW\, etc.\n\n[This is joint work with Gerard Hooghiemstra\, Sha
 nkar Bhamidi\, Piet Van Mieghem\, Henri van den Esker and Dmitri Znamenski
 .]\n
LOCATION:Seminar Room 1\, Newton Institute
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