Complexity of gradient projection method for optimal routing in data networks

Abstract

Derives a time complexity bound for the gradient projection method for optimal routing in data networks. This result shows that the gradient projection algorithm of the Goldstein-Levitin-Poljak type formulated by Bertsekas (1982) converges to within /spl epsiv/ in relative accuracy in O(/spl epsiv//sup 2/h/sub min/N/sub max//sup L/) iterations, where N/sub max//sup L/ is the number of paths sharing the maximally shared link, and h/sub min/ is the diameter of the network. Based on this complexity result, the authors 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 [Bertsekas, 1982], where n is the number of nodes in the network. The result of the paper argues for constructing networks with low diameter for the purpose of reducing the complexity of the network control algorithms. The result also implies that parallelizing the optimal rotating algorithm over the network nodes is beneficial.