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Bounding the maximum size of a packet radio network

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1 Author(s)
C. G. Prohazka ; IBM, Research Triange Park, NC, USA

The author addresses the problem, arising in the topology design of packet radio networks (PRNs) which use time-division multiplexing and have a diameter constraint, of what is the maximum number nc(f,k) of users which can be contained in a diameter-k PRN with f time slots per frame. The author assumed that users cannot transmit and receive simultaneously and cannot transmit/receive more than one packet at a time. This assumption implies that no two channels accessed by the same user may be assigned the same time slot. It is shown that the problem of determining nc(f,k) is identical to the problem of determining the largest number of vertices which can be contained in an f-edge colorable directed graph with diameter k. Lower bounds on nc(f, k) for f/2, k=3, 4, 5, . . . are obtained by generating large graphs of this type. The graphs are constructed and colored by simple and fast procedures which are similar for different values of f and k. An extensive bibliography on the edge-coloring problem is included

Published in:

IEEE Transactions on Computers  (Volume:37 ,  Issue: 10 )