Distributed fault tolerant computation of weakly connected dominating set in ad hoc networks

Our purpose in this paper is to propose a self-stabilizing protocol for weakly connected dominating set (WCDS) set in a given ad hoc network graph. WCDS is a particular variant of graph domination predicates which play an important role in routing in ad hoc networks. There are many variants of domination problems in bidirectional networks; WCDS is also useful in forming clusters in ad hoc networks. There are many heuristic and distributed algorithms to compute WCDS in network graphs while almost all of them will need complete information about the network topology and most of them are not fault tolerant or mobility tolerant. Self-stabilization is a protocol design paradigm that is especially useful in resource constrained infrastructure-less networks since nodes can make moves based on local knowledge only and yet a global task is accomplished in a fault tolerant manner; it also facilitates for nodes to enter and exit the network freely. There exist self-stabilizing protocols for minimal spanning tree, total domination, and others. We have shown that the paradigm is capable of designing a protocol for WCDS. Our objective is to mathematically prove the correctness and the convergence of the protocol in any worst-case scenario, as is usually done for self-stabilizing protocols for other graph predicates used for ad hoc networks.