## Abstract

Interval routing is a compact way for representing routing tables on a graph. It is based on grouping together, in each node, destination addresses that use the same outgoing edge in the routing table. Such groups of addresses are represented by some intervals of consecutive integers. We show that almost all the graphs, i.e., a fraction of at least 1 – 1/n^{2} of all the n-node graphs, support a shortest path interval routing with at most three intervals per outgoing edge, even if the addresses of the nodes are arbitrarily fixed in advance and cannot be chosen by the designer of the routing scheme. In case the addresses are initialized randomly, we show that two intervals per outgoing edge suffice, and conversely, that two intervals are required, for almost all graphs. Finally, if the node addresses can be chosen as desired, we show how to design in polynomial time a shortest path interval routing with a single interval per outgoing edge, for all but at most O(log^{3} n) outgoing edges in each node. It follows that almost all graphs support a shortest path routing scheme which requires at most n + O(log^{4} n) bits of routing information per node, improving on the previous upper bound.

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

Title of host publication | Distributed Computing - 12th International Symposium, DISC 1998, Proceedings |

Editors | Shay Kutten, Shay Kutten |

Publisher | Springer Verlag |

Pages | 161-174 |

Number of pages | 14 |

ISBN (Print) | 3540650660, 9783540650669 |

DOIs | |

State | Published - 1998 |

Externally published | Yes |

Event | 12th International Symposium on Distributed Computing, DISC 1998 - Andros, Greece Duration: 24 Sep 1998 → 26 Sep 1998 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 1499 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 12th International Symposium on Distributed Computing, DISC 1998 |
---|---|

Country/Territory | Greece |

City | Andros |

Period | 24/09/98 → 26/09/98 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 1998.