### 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) |
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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 |

### Keywords

- Efficient approximation algorithms
- Multiple additive constraints
- QoS routing

### ASJC Scopus subject areas

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

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## Cite this

*IEEE/ACM Transactions on Networking*,

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