group5 - small worlds in mobile networks: state of the art,...

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small worlds in mobile networks: state of the art, applications March 24 th 2010 CISE, University of Florida
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group 5 Ashish Kartheek Kedar Supriya Vidhyaa
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outline kedar what is a small world? six degrees of separation small world networks small world search problem its a big world? kartheek relational v/s spatial graphs Effect of mobility on overlaying small world networks over MANETs Applicability of small worlds to relational/ spatial graphs examples vidhyaa Towards Hierarchical Routing in Small World Wireless Networks
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what is a small world? Travers, Jeffrey & Stanley Milgram. 1969. "An Experimental Study of the Small World Problem." Sociometry, Vol. 32, No. 4, pp. 425-443.
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the small world experiment Jeffrey Travers, Stanley Milgram Chain letters from NE and Boston, MA to Sharon, MA Mean path length- 5.2 Sociometric "stars" Convergence of chains The world is a social network with short path lengths
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idea #1
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1. six degrees of separation Six degrees of separation between us and everyone else on this planet.
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Applications: Erdős number collaborative distance between a mathematician and Paul Erdős. measured by coauthorship of papers a measure of mathematical prominence
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Erdős number
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Applications: Bacon Number trivia game "six degrees of Kevin Bacon" Erdős Bacon number sixdegrees.org a charitable social network
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oracle of bacon
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Applications: Social Networks people you may know friend finder
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idea #2 Watts, D.J.; Strogatz, S.H. (1998). "Collective dynamics of 'small-world' networks.". Nature 393 (6684): 409–10. doi:10.1038/30918. PMID 9623998.
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2. small world networks Duncan J. Watts, Principal Research Scientist, Yahoo! Research Steve Strogatz Professor, Cornell University the Watts and Strogatz Model
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ordered/regular model high clustering high average path length
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random model low clustering low average path length
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rewiring- small world model high clustering low average path length
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rewiring algorithm say the graph has n vertices with each vertex connected to its k nearest neighbors level=1 do for (i=0; i<=n; i++ ) {
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algorithm execution: for a graph with n vertices each connected to its k nearest neighbors, total edges in graph = n.k/2 total iterations = k/2 in the intermediate region: where 0< p <1 , the graph is a small world graph
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transition to small worlds: a broad interval where average path length falls but clustering remains same short cuts transition is undetected at local level
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applications small worlds is a generic phenomenon in nature actor collaboration US power grid neural network of C. Elagens human brain? disease spread mapped as explicit function of network structure future multi-disciplinary research
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idea #3 Watts, D.J.; Six Degrees: the science of a connected age (2004 in paperback, ISBN 0-393-32542-3 and 2003 in hardcover, ISBN 0-393-04142-5) J. Kleinberg. The Small-World Phenomenon and Decentralized Search.
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This note was uploaded on 05/27/2011 for the course CIS 4930 taught by Professor Staff during the Spring '08 term at University of Florida.

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group5 - small worlds in mobile networks: state of the art,...

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