## Abstract

This paper presents a routing strategy called Pivot Interval Routing (PIR), which allows message routing on every weighted n-node network along paths whose stretch factor (namely, the ratio between the length of the routing path and the shortest path) is at most five, and whose average stretch factor is at most three, with routing tables of size O(√n log^{3/2}n) bits per node. In addition, the route lengths are at most 2D ([1.5D] for uniform weights) where D is the weighted diameter of the network. Moreover, it is shown that the PIR strategy can be constructed in polynomial time and can be implemented so that the generated scheme is in the form of an interval routing scheme (IRS), using at most O(√n log n) intervals per link. As a result, the schemes are simpler than previous ones and they imply that the paths followed by messages are loop-free. On the other hand, we show that there is no loop-free routing strategy guaranteeing a memory bound of at most √n bits per node for all networks, regardless of the route lengths.

Original language | English |
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Pages (from-to) | 97-114 |

Number of pages | 18 |

Journal | Journal of Algorithms |

Volume | 46 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2003 |

Externally published | Yes |

### Bibliographical note

Funding Information:✩ An extended abstract of this paper has appeared in the PODC ’98 symposium. * Corresponding author. E-mail addresses: eilamt@us.ibm.com (T. Eilam), gavoille@labri.fr (C. Gavoille), peleg@wisdom.weizmann.ac.il, david.peleg@weizmann.ac.il (D. Peleg). 1 Supported in part by grants from the Israel Science Foundation and from the Israel Ministry of Science and