Self-stabilizing unidirectional network algorithms by power supply

Power supply, a surprisingly simple and new general paradigm for the development of self-stabilizing algorithms in different models, is introduced. The paradigm is exemplified by developing simple and efficient self-stabilizing algorithms for leader election and either breadth-first search or depth-first search spanning-tree constructions, in strongly connected unidirectional and bidirectional dynamic networks (synchronous and asynchronous). The different algorithms stabilize in O(n) time in both synchronous and asynchronous networks without assuming any knowledge of the network topology or size, where n is the total number of nodes. Following the leader election algorithms, we present a generic self-stabilizing spanning tree and/or leader election algorithm that produces a whole spectrum of new and efficient algorithms for these problems. Two variations that produce either a rooted depth-first search tree or a rooted breadth-first search tree are presented.