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The Weight and Hopcount of the Shortest Path in the Complete Graph with Exponential Weights

Published online by Cambridge University Press:  01 July 2008

GERARD HOOGHIEMSTRA  and
PIET VAN MIEGHEM
GERARD HOOGHIEMSTRA
Affiliation:
Delft University of Technology, Electrical Engineering, Mathematics and Computer Science, PO Box 5031, 2600 GA Delft, The Netherlands (e-mail: G.Hooghiemstra@ewi.tudelft.nl, P.VanMieghem@ewi.tudelft.nl)
PIET VAN MIEGHEM
Affiliation:
Delft University of Technology, Electrical Engineering, Mathematics and Computer Science, PO Box 5031, 2600 GA Delft, The Netherlands (e-mail: G.Hooghiemstra@ewi.tudelft.nl, P.VanMieghem@ewi.tudelft.nl)
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Abstract

Both the hopcount HN (the number of links) and the weight WN (the sum of the weights on links) of the shortest path between two arbitrary nodes in the complete graph KN with i.i.d. exponential link weights is computed. We consider the joint distribution of the pair (HN, WN) and derive, after proper scaling, the joint limiting distribution. One of the results is that HN and WN, properly scaled, are asymptotically independent.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 4 , July 2008 , pp. 537 - 548
Copyright
Copyright © Cambridge University Press 2008

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