Chapter

Automata, Languages and Programming

Volume 2076 of the series Lecture Notes in Computer Science pp 757-772

Date:

Routing in Trees

  • Pierre FraigniaudAffiliated withCNRS, Laboratoire de Recherche en Informatique, Université Paris-Sud
  • , Cyril GavoilleAffiliated withLaboratoire Bordelais de Recherche en Informatique, Université Bordeaux I

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Abstract

This article focuses on routing messages along shortest paths in tree networks, using compact distributed data structures. We mainly prove that n-node trees support routing schemes with message headers, node addresses, and local memory space of size O(log n) bits, and such that every local routing decision is taken in constant time. This improves the best known routing scheme by a factor of O(log n) in term of both memory requirements and routing time. Our routing scheme requires headers and addresses of size slightly larger than log n, motivated by an inherent trade-off between address-size and memory space, i.e., any routing scheme with addresses on log n bits requires Ω(√n) bits of local memory-space. This shows that a little variation of the address size, e.g., by an additive O(log n) bits factor, has a significant impact on the local memory space.

Keywords

compact routing trees routing algorithms