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doi:10.1016/0012-365X(95)94025-8 
Copyright © 1995 Published by Elsevier Science B.V.
An efficient algorithm to find optimal double loop networks*1
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Received 7 July 1993;
Abstract
The problem of finding optimal diameter double loop networks with a fixed number of vertices has been widely studied. In this work, we give an algorithmic solution of the problem by using a geometrical approach.
Given a fixed number of vertices n, the general problem is to find “steps”
, such that the digraph G(n; s1, s2) with set of vertices
and adjacencies given by i → i + s1 (mod n) and i → i + s2 (mod n) has minimum diameter d(n). A lower bound of this diameter is known to be be lb(n)=
√3n
−2. So, given n, the algorithm has as outputs s1,s2 and the minimum integer κ = κ(n) such that d(n;s1,s2)=d(n)=lb(n)+κ
The running time complexity of the algorithm is O(κ3)O(logn)-O(κ) is unknown but it is upper-bounded by O(4√n).
Moreover, in most of the cases the algorithm also gives (as a by-product) an infinite family of digraphs with increasing order and diameter as above, to which the obtained digraph G(n; S1,S2) belongs.
Article Outline
*1 Work supported by the Spanish Research Council (Comisión Interministerial de Ciencia y Tecnologia, CICYT) under project TIC90-0712.
