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A General Approach to L(h,k)-Label Interconnection Networks

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Abstract

Given two non-negative integers h and k, an L(h, k)-labeling of a graph G = (V, E) is a function from the set V to a set of colors, such that adjacent nodes take colors at distance at least h, and nodes at distance 2 take colors at distance at least k. The aim of the L(h, k)-labeling problem is to minimize the greatest used color. Since the decisional version of this problem is NP-complete, it is important to investigate particular classes of graphs for which the problem can be efficiently solved. It is well known that the most common interconnection topologies, such as Butterfly-like, Bene·s, CCC, Trivalent Cayley networks, are all characterized by a similar structure: they have nodes organized as a matrix and connections are divided into layers. So we naturally introduce a new class of graphs, called (l × n)-multistage graphs, containing the most common interconnection topologies, on which we study the L(h, k)-labeling. A general algorithm for L(h, k)-labeling these graphs is presented, and from this method an efficient L(2, 1)-labeling for Butterfly and CCC networks is derived. Finally we describe a possible generalization of our approach.

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Authors and Affiliations

  1. Department of Computer Science, Sapienza University of Rome, Rome, Italy

    Tiziana Calamoneri, Saverio Caminiti & Rossella Petreschi

Authors
  1. Tiziana Calamoneri
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  2. Saverio Caminiti
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  3. Rossella Petreschi
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Corresponding author

Correspondence to Tiziana Calamoneri.

Additional information

Work supported in part by Sapienza University of Rome (project “Parallel and Distributed Codes”).

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Calamoneri, T., Caminiti, S. & Petreschi, R. A General Approach to L(h,k)-Label Interconnection Networks. J. Comput. Sci. Technol. 23, 652–659 (2008). https://doi.org/10.1007/s11390-008-9161-8

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  • DOI: https://doi.org/10.1007/s11390-008-9161-8

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