### Abstract

A fundamental problem in quality-of-service (QoS) routing is to find a path between a source- destination node pair that satisfies two or more end-to-end QoS constraints. We model this problem using a graph with n vertices and edges with K additive QoS parameters associated with each edge, for any constant K ≥ 2. This problem is known to be NP-hard. Fully polynomial time approximation schemes (FPTAS) for the case of K = 2 have been reported in the literature. We concentrate on the general case and make the following contributions. 1) We present a very simple O(Km + n log n) time K-approximation algorithm that can be used in hop-by-hop routing protocols. 2) We present an FPTAS for one optimization version of the QoS routing problem with a time complexity of O(m (n/ε)^{K-1}). 3) We present an FPTAS for another optimization version of the QoS routing problem with a time complexity of O(n log n + m (H/ε)^{K-1}) when there exists an H-hop path satisfying all QoS constraints. When K is reduced to 2, our results compare favorably with existing algorithms. The results of this paper hold for both directed and undirected graphs. For ease of presentation, undirected graph is used.

Original language | English (US) |
---|---|

Pages (from-to) | 201-211 |

Number of pages | 11 |

Journal | IEEE/ACM Transactions on Networking |

Volume | 15 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2007 |

### Fingerprint

### Keywords

- Efficient approximation algorithms
- Multiple additive constraints
- QoS routing

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Hardware and Architecture
- Information Systems

### Cite this

*IEEE/ACM Transactions on Networking*,

*15*(1), 201-211. https://doi.org/10.1109/TNET.2006.890089

**Finding a path subject to many additive QoS constraints.** / Xue, Guoliang; Sen, Arunabha; Zhang, Weiyi; Tang, Jian; Thulasiraman, Krishnaiya.

Research output: Contribution to journal › Article

*IEEE/ACM Transactions on Networking*, vol. 15, no. 1, pp. 201-211. https://doi.org/10.1109/TNET.2006.890089

}

TY - JOUR

T1 - Finding a path subject to many additive QoS constraints

AU - Xue, Guoliang

AU - Sen, Arunabha

AU - Zhang, Weiyi

AU - Tang, Jian

AU - Thulasiraman, Krishnaiya

PY - 2007/2

Y1 - 2007/2

N2 - A fundamental problem in quality-of-service (QoS) routing is to find a path between a source- destination node pair that satisfies two or more end-to-end QoS constraints. We model this problem using a graph with n vertices and edges with K additive QoS parameters associated with each edge, for any constant K ≥ 2. This problem is known to be NP-hard. Fully polynomial time approximation schemes (FPTAS) for the case of K = 2 have been reported in the literature. We concentrate on the general case and make the following contributions. 1) We present a very simple O(Km + n log n) time K-approximation algorithm that can be used in hop-by-hop routing protocols. 2) We present an FPTAS for one optimization version of the QoS routing problem with a time complexity of O(m (n/ε)K-1). 3) We present an FPTAS for another optimization version of the QoS routing problem with a time complexity of O(n log n + m (H/ε)K-1) when there exists an H-hop path satisfying all QoS constraints. When K is reduced to 2, our results compare favorably with existing algorithms. The results of this paper hold for both directed and undirected graphs. For ease of presentation, undirected graph is used.

AB - A fundamental problem in quality-of-service (QoS) routing is to find a path between a source- destination node pair that satisfies two or more end-to-end QoS constraints. We model this problem using a graph with n vertices and edges with K additive QoS parameters associated with each edge, for any constant K ≥ 2. This problem is known to be NP-hard. Fully polynomial time approximation schemes (FPTAS) for the case of K = 2 have been reported in the literature. We concentrate on the general case and make the following contributions. 1) We present a very simple O(Km + n log n) time K-approximation algorithm that can be used in hop-by-hop routing protocols. 2) We present an FPTAS for one optimization version of the QoS routing problem with a time complexity of O(m (n/ε)K-1). 3) We present an FPTAS for another optimization version of the QoS routing problem with a time complexity of O(n log n + m (H/ε)K-1) when there exists an H-hop path satisfying all QoS constraints. When K is reduced to 2, our results compare favorably with existing algorithms. The results of this paper hold for both directed and undirected graphs. For ease of presentation, undirected graph is used.

KW - Efficient approximation algorithms

KW - Multiple additive constraints

KW - QoS routing

UR - http://www.scopus.com/inward/record.url?scp=33947538745&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33947538745&partnerID=8YFLogxK

U2 - 10.1109/TNET.2006.890089

DO - 10.1109/TNET.2006.890089

M3 - Article

AN - SCOPUS:33947538745

VL - 15

SP - 201

EP - 211

JO - IEEE/ACM Transactions on Networking

JF - IEEE/ACM Transactions on Networking

SN - 1063-6692

IS - 1

ER -