Complexity of gradient projection method for optimal routing in data networks

Wei K. Tsai, John K. Antonio, Garng Morton Huang

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

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 the Goldstein-Levitin-Poljak type formulated by Bertsekas 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.

Original languageEnglish
Pages (from-to)897-905
Number of pages9
JournalIEEE/ACM Transactions on Networking
Volume7
Issue number6
DOIs
Publication statusPublished - 1 Dec 1999
Externally publishedYes

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Routing algorithms

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Electrical and Electronic Engineering

Cite this

Complexity of gradient projection method for optimal routing in data networks. / Tsai, Wei K.; Antonio, John K.; Huang, Garng Morton.

In: IEEE/ACM Transactions on Networking, Vol. 7, No. 6, 01.12.1999, p. 897-905.

Research output: Contribution to journalArticle

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