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Journal of Computer Science and Technology

, Volume 23, Issue 4, pp 652–659 | Cite as

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

  • Tiziana CalamoneriEmail author
  • Saverio Caminiti
  • Rossella Petreschi
Short Paper

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.

Keywords

multistage interconnection network L(h, k)-labeling channel assignment problem 

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Copyright information

© Springer 2008

Authors and Affiliations

  • Tiziana Calamoneri
    • 1
    Email author
  • Saverio Caminiti
    • 1
  • Rossella Petreschi
    • 1
  1. 1.Department of Computer ScienceSapienza University of RomeRomeItaly

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