Exploration of path space using sensor network geometry

In a sensor network there are many paths between a source and a destination. An efficient method to explore and navigate in the `path space' can help many important routing primitives, in particular, multipath routing and resilient routing (when nodes or links can fail unexpectedly) as considered in this paper. Both problems are challenging for a general graph setting, especially if each node cannot afford to have the global knowledge. In this paper we use a geometric approach to allow efficient exploration of the path space with very little overhead. We are motivated by the recent development on regulating a sensor network geometry using conformal mapping, in which any sensor network can be embedded to be circular (and any possible hole is made circular as well) and greedy routing guarantees delivery. In this paper we explore the freedom of a Möbius transformation inherent to this conformal mapping. By applying a Möbius transformation we can get an alternative embedding with the same property such that greedy routing generates a different path. We present distributed algorithms using local information and limited global information (the positions and sizes of the holes) to generate disjoint multi-paths for a given source destination pair or switch to a different path `on the fly' when transmission failure is encountered. The overhead of applying a Möbius transformation simply boils down to four parameters that could be carried by a packet or determined at need at the source. Demonstrated by simulation results, this method compares favorably in terms of performance and cost metrics with centralized solutions of using flow algorithms or random walk based decentralized solutions in generating alternative paths.