Self-stabilizing optimal local routing in ad hoc networks

Given a wireless mobile ad hoc network (MANET), we present a self-stabilizing optimal local routing (SOLR) algorithm. Our claim of optimality is based on the minimum distance. The optimal routing is done with respect to the t closest nodes (called t-set). The locality is maintained with respect to the t-set, not with the direct neighbors. The algorithm is transparent to what the distance means: can be either the real distance, or the number of hops. The value of t is application dependent, and is decided in advance. t is n (where n is the upper bound on the maximum number of nodes in the network) when each node needs to know the shortest paths to all other nodes. t is less than n when nodes need to know the network only partially. A self-stabilizing system has the ability to automatically recover to normal behavior in case of transient faults, without a centralized control. Each node can start in some arbitrary state and with no knowledge of the network architecture, but still eventually computes a correct routing table for the t-closest nodes (t-set). The space complexity per node of SOLR, is O((t+δ)log(n)) bits (where δ is the node degree) with a total of O(n(t+Δ)log(n)) bits (where Δ is the maximum node degree) for the whole network. The stabilization time of the SOLR, algorithm is O(d+c) time units (where d is the network diameter and c is a large constant depending on some local computation). SOLR, can easily work for optimal on-demand routing by considering the set of nodes for which the shortest paths are desired instead of the t closest nodes. Also, it can be extended to a global routing protocol by using features specific to other protocols (e.g., hierarchical routing, cluster routing, interval routing, etc.).