## Abstract

A fundamental problem in quality-of-service (QoS) routing is the multiconstrained path (MCP) problem, where one seeks a source-destination path satisfying K > 2 additive QoS constraints in a network with K additive QoS parameters. The MCP problem is known to be NP-complete. One popular approach is to use the shortest path with respect to a single edge weighting function as an approximate solution to MCP. In a pioneering work, Jaffe showed that the shortest path with respect to a scaled 1-norm of the K edge weights is a 2-approximation to MCP in the sense that the sum of the larger of the path weight and its corresponding constraint is within a factor of 2 from minimum. In a recent paper, Xue et al. showed that the shortest path with respect to a scaled ∞-norm of the K edge weights is a K-approximation to MCP, in the sense that the largest ratio of the path weight over its corresponding constraint is within a factor of K from minimum. In this paper, we study the relationship between these two optimization criteria and present a class of provably good approximation algorithms to MCP. We first prove that a good approximation according to the second optimization criterion is also a good approximation according to the first optimization criterion, but not vice versa. We then present a class of very simple K-approximation algorithms according to the second optimization criterion, based on the computation of a shortest path with respect to a single edge weighting function.

Original language | English (US) |
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Pages (from-to) | 859-863 |

Number of pages | 5 |

Journal | IEEE Transactions on Computers |

Volume | 56 |

Issue number | 6 |

DOIs | |

State | Published - Jul 7 2007 |

## Keywords

- approximation algorithms
- multiple additive QoS parameters
- QoS routing
- scaled p-norm

## ASJC Scopus subject areas

- Theoretical Computer Science
- Software
- Hardware and Architecture
- Computational Theory and Mathematics