An all-to-all routing in a graph G is a set of oriented paths of G, with
exactly one path for each ordered pair of vertices. The load of an edge under
an all-to-all routing R is the number of times it is used (in either
direction) by paths of R, and the maximum load of an edge is denoted by
π(G,R). The edge-forwarding index π(G) is the minimum of π(G,R)
over all possible all-to-all routings R, and the arc-forwarding index
Ï€(G) is defined similarly by taking direction into
consideration, where an arc is an ordered pair of adjacent vertices. Denote by
w(G,R) the minimum number of colours required to colour the paths of R such
that any two paths having an edge in common receive distinct colours. The
optical index w(G) is defined to be the minimum of w(G,R) over all possible
R, and the directed optical index w(G) is defined
similarly by requiring that any two paths having an arc in common receive
distinct colours. In this paper we obtain lower and upper bounds on these four
invariants for 4-regular circulant graphs with connection set {±1,±s}, 1<s<n/2. We give approximation algorithms with performance ratio a
small constant for the corresponding forwarding index and routing and
wavelength assignment problems for some families of 4-regular circulant
graphs.Comment: 19 pages, no figure in Journal of Discrete Algorithms 201