Link Fault Localization Using Bi-Directional M-Trails in All-Optical Mesh Networks

The paper considers the problem of single-link failure localization in all-optical mesh networks. Our study follows a generic monitoring approach using supervisory lightpaths (S-LPs), in which a set of bi-directional monitoring trails (bm-trails) are defined and closely monitored, such that the network controller can achieve unambiguous failure localization (UFL) for any single link by collecting the flooded alarms from the affected bm-trails. With a target of minimizing the number of bm-trails (or the length of alarm codes) required for single-link UFL, the paper provides optimal (or essentially optimal) solutions to the bm-trail allocation problem on a number of well known topologies. First we demonstrate that the theoretical lower bound of [log
₂
(|E|+1)] bm-trails can be achieved in any 2 · [{ log
₂
{(|E|+1)} }] connected graph, where |E| is the number of links. Next, we prove an essentially optimal solution for 1-by-N grid topologies (also known as chocolate bar graphs), where [{0.42+ log
₂
{(|E|+2)}}] bm-trails can be achieved. Based on the solution for chocolate bars, we further investigate bm-trail solutions to general 2-dimensional (2D) grid topologies, and the developed solution requires no more than 3+[ log
₂
(|E|+1)] bm-trails for UFL. Such an optimal (or essentially optimal) logarithmic behavior, although has been well observed in general topologies in our previous studies , is formalized for the first time in this paper via a suite of polynomial-time deterministic constructions that consume less than a few seconds of running time in topologies of thousands of nodes.