Optimal Solutions for Single Fault Localization in Two Dimensional Lattice Networks

Achieving fast, precise, and scalable fault localization has long been a highly desired feature in all-optical mesh networks. Monitoring tree (m-tree) is an interesting method that has been introduced as the most general monitoring structure for achieving unambiguous failure localization (UFL). Ideally, with J m-trees one can monitor up to 2^J-1 links when a single failure has to be located. Such a logarithmic behavior has also been observed in numerous case studies of real life network topologies. It is expected that the m-tree framework will lead to a highly scalable link failure monitoring mechanism for not only all-optical mesh networks, but any possible future information system with mesh topologies, such as all-optical mesh networks, touch panels, quantum computing, and VLSI. It is an important task to investigate the extent such an optimal logarithmic behavior may hold, in particular in practically relevant network topologies. As an endeavor toward this goal, the paper investigates the problem by identifying essentially tight logarithmic bounds for two dimensional lattice networks. Experiments are conducted to show the feasibility and performance of the proposed constructions.