By Topic

Complexity of gradient projection method for optimal routing in data networks

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Tsai, W.K. ; Dept. of Electr. & Comput. Eng., California Univ., Irvine, CA, USA ; Antonio, John K. ; Huang, G.M.

In this paper, we derive a time-complexity bound for the gradient projection method for optimal routing in data networks. This result shows that the gradient projection algorithm of Goldstein-Levitin-Poljak type formulated by Bertsekas (1982), Bertsekas and Gallager (1987) and Bertsekas et al. (1984) converges to within ε in relative accuracy in O(ε-2hminNmax) number of iterations, where Nmax is the number of paths sharing the maximally shared link, and hmin is the diameter of the network. Based on this complexity result, we also show that the one-source-at-a-time update policy has a complexity bound which is O(n) times smaller than that of the all-at-a-time update policy, where n is the number of nodes in the network. The result of this paper argues for constructing networks with low diameter for the purpose of reducing complexity of the network control algorithms. The result also implies that parallelizing the optimal routing algorithm over the network nodes is beneficial

Published in:

Networking, IEEE/ACM Transactions on  (Volume:7 ,  Issue: 6 )