### 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^{-2}h_{min}N_{max}) number of iterations, where N_{max} is the number of paths sharing the maximally shared link, and h_{min} 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 language | English |
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Pages (from-to) | 897-905 |

Number of pages | 9 |

Journal | IEEE/ACM Transactions on Networking |

Volume | 7 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1 Dec 1999 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*IEEE/ACM Transactions on Networking*,

*7*(6), 897-905. https://doi.org/10.1109/90.811454

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

Research output: Contribution to journal › Article

*IEEE/ACM Transactions on Networking*, vol. 7, no. 6, pp. 897-905. https://doi.org/10.1109/90.811454

}

TY - JOUR

T1 - Complexity of gradient projection method for optimal routing in data networks

AU - Tsai, Wei K.

AU - Antonio, John K.

AU - Huang, Garng Morton

PY - 1999/12/1

Y1 - 1999/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0033310545&partnerID=8YFLogxK

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U2 - 10.1109/90.811454

DO - 10.1109/90.811454

M3 - Article

AN - SCOPUS:0033310545

VL - 7

SP - 897

EP - 905

JO - IEEE/ACM Transactions on Networking

JF - IEEE/ACM Transactions on Networking

SN - 1063-6692

IS - 6

ER -