Constructions for unambiguous node failure localization in grid topologies

Precise, fast and scalable fault localization is a highly desired feature in all optical mesh networks. The monitoring trail (m-trail) framework has been long in use for centralized failure localization, its capabilities were recently utilized to accommodate the distributed scenario as well. Most of the prior art focused solely on link failures; in this study we step further and analyze node failures only. Node failures are fundamentally different from link failures, and thus a new theoretical framework is developed. In particular, we are interested in the scalability of localizing node failures. From an information theoretic view, with b m-trails at most 2^b -1 single failures can be identified. This intuitively leads to a very attractive property that the number of monitors might be logarithmic to the size of the network. Does this logarithmic behaviour holds for real life topologies too? As a step towards the answer, we show tight constructions for both centralized and distributed node failure localization.