The weight and hopcount of the shortest path in the complete graph with exponential weights

Authors:
Gerard Hooghiemstra;Piet Van mieghem
Affiliations:
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.tudel ...;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.tudel ...
Venue:
Combinatorics, Probability and Computing
Year:
2008

Citing 4
Cited 2

One, Two and Three Times log n/n for Paths in a Complete Graph with Random Weights

Combinatorics, Probability and Computing
Performance Analysis of Communications Networks and Systems

Performance Analysis of Communications Networks and Systems
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Weight of the shortest path to the first encountered peer in a peer group of size m

Probability in the Engineering and Informational Sciences

The longest minimum-weight path in a complete graph

Combinatorics, Probability and Computing
The effect of peer selection with hopcount or delay constraint on peer-to-peer networking

NETWORKING'08 Proceedings of the 7th international IFIP-TC6 networking conference on AdHoc and sensor networks, wireless networks, next generation internet

Quantified Score

Hi-index	0.00

Visualization

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.