### 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 s in relative accuracy in O (ε
^{2}h
_{min}-N
_{max}
^{L}) iterations, where N
_{max}
^{L} is the number of paths sharing the maximally shared link, and h
_{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

Original language | English |
---|---|

Title of host publication | INFOCOM'95 - 14th Annual Joint Conference of the IEEE Computer and Communications Societies |

Pages | 269-277 |

Number of pages | 9 |

Volume | 1 |

DOIs | |

Publication status | Published - 1 Dec 1995 |

Externally published | Yes |

Event | INFOCOM'95 - 14th Annual Joint Conference of the IEEE Computer and Communications Societies - Boston, MA, United States Duration: 2 Apr 1995 → 6 Apr 1995 |

### Other

Other | INFOCOM'95 - 14th Annual Joint Conference of the IEEE Computer and Communications Societies |
---|---|

Country | United States |

City | Boston, MA |

Period | 2/4/95 → 6/4/95 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Electrical and Electronic Engineering

### Cite this

*INFOCOM'95 - 14th Annual Joint Conference of the IEEE Computer and Communications Societies*(Vol. 1, pp. 269-277). [515885] https://doi.org/10.1109/INFCOM.1995.515885

**Complexity of gradient projection method for optimal routing indata networks.** / Tsai, W. K.; Antonio, J. K.; Huang, Garng Morton.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*INFOCOM'95 - 14th Annual Joint Conference of the IEEE Computer and Communications Societies.*vol. 1, 515885, pp. 269-277, INFOCOM'95 - 14th Annual Joint Conference of the IEEE Computer and Communications Societies, Boston, MA, United States, 2/4/95. https://doi.org/10.1109/INFCOM.1995.515885

}

TY - GEN

T1 - Complexity of gradient projection method for optimal routing indata networks

AU - Tsai, W. K.

AU - Antonio, J. K.

AU - Huang, Garng Morton

PY - 1995/12/1

Y1 - 1995/12/1

N2 - 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 s in relative accuracy in O (ε 2h min-N max L) iterations, where N max L is the number of paths sharing the maximally shared link, and h 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

AB - 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 s in relative accuracy in O (ε 2h min-N max L) iterations, where N max L is the number of paths sharing the maximally shared link, and h 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

UR - http://www.scopus.com/inward/record.url?scp=61849158285&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=61849158285&partnerID=8YFLogxK

U2 - 10.1109/INFCOM.1995.515885

DO - 10.1109/INFCOM.1995.515885

M3 - Conference contribution

AN - SCOPUS:61849158285

SN - 081866990X

SN - 9780818669903

VL - 1

SP - 269

EP - 277

BT - INFOCOM'95 - 14th Annual Joint Conference of the IEEE Computer and Communications Societies

ER -