Computing the Diameter in Multiple-Loop Networks

Abstract A multiple-loop network is an undirected Cayley graph of a cyclic group. Algorithms for computing the diameter of multiple-loop networks are discussed. By a geometrical approach the problem of computing the diameter of a multiple-loop network (with k hops) is transformed to an equivalent problem in the integer lattice Z k . In the special case of double-loop networks this leads to an algorithm with running time O (log n ). This is an undirected analogue to the result of Cheng and Hwang, who recently found an O (log n ) algorithm for computing diameters of directed double-loop networks.