## Abstract

In designing a routing scheme for a communication network it is desirable to use as short as possible paths for routing messages, while keeping the routing information stored in the processors' local memory as succinct as possible. The efficiency of a routing scheme is measured in terms of its stretch factor-the maximum ratio between the cost of a route computed by the scheme and that of a cheapest path connecting the same pair of vertices. This paper presents several simple families of routing schemes for general networks, featuring some desirable properties. Our two main families are the hierarchical covering pivots schemes HCP_{k} and the hierarchical balanced schemes HB_{k} (for k ≥ 1). The scheme HCP_{k} guarantees a stretch factor of 2^{k} - 1 and requires storing a total of O(k · n^{1 + 1 k}log^{2} n) bits of routing information in the network. The new important features of these schemes are applicability to networks with arbitrary edge costs and attractive stretch factors for small values of k. The purpose of the second method is to provide balanced bounds on the memory requirements of the individual vertices. The scheme HB_{k} guarantees a stretch factor of 2 · 3^{k} - 1 and requires storing at most O(k log n(d + n^{ 1 k})) bits of routing information in a vertex of degree d and O(kn^{1 + 1 k}log n) bits overall. We also describe an efficient distributed preprocessing algorithm for this scheme, which requires same amount of space.

Original language | English |
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Pages (from-to) | 307-341 |

Number of pages | 35 |

Journal | Journal of Algorithms |

Volume | 11 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1990 |

### Bibliographical note

Funding Information:DAVID PELEG$ Mathematics, The Weiunann Institute, Rehovot 76100, Israel Received February 2,199O In designing a routing scheme for a communication network it is desirable to use as short as possible paths for routing messages, while keeping the routing information stored in the processors’ local memory as succinct as possible. The efftciency of a routing scheme is measured in terms of its stretch factor-the maximum ratio between the cost of a route computed by the scheme and that of a cheapest path connecting the same pair of vertices. This paper presents several simple families of routing schemes for general networks, featuring some desirable properties. Our two main families are the hierarchical covering pi&s schemes HCP, and the hierarchical balanced schemes HB, (for k t 1). The scheme HCP, guarantees a stretch factor of 2’ - 1 and requires storing a total of O(k . n’+l/k log’n) bits of routing information in the network. The new important *Supported by Air Force Contract TNDGAFOSR-860078, AR0 Contract DAALO3-86-K-0171, NSF Contract CCR8611442, and a special grant from IBM. ‘Supported in part by a Weizmann fellowship, by Contract ONR NOOO14-88-K-0166 and by ant of Stanford Center for Integrated Systems. “Q Part of this work was carried out while this author was visiting Stanford University. Supported in part by a Weizmann fellowship, by Contract ONR N00014-88-K-0166 and by a grant of Stanford Center for Integrated Systems.