Special Issue: Computer Networks and Distributed Computing

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A General Approach to {\it\bfseries L$($h,k$)$}-Label Interconnection Networks

Tiziana Calamoneri, Saverio Caminiti, and Rossella Petreschi   

  1. Department of Computer Science, Sapienza University of Rome, Italy
  • Received:2007-03-22 Revised:2008-04-24 Online:2008-07-10 Published:2008-07-10

Given two non-negative integers $h$ and $k$, an $L(h,k)$-{\em 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\v{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 $(l \times n)$-{\em 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.

Key words: logic for artificial intelligence(AI); automated theorem proving; logic programming; Horn and non-Horn sets; predicate renaming; NP-completeness;


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