Distributed Maintenance of a Spanning Tree Using Labeled Tree Encoding

Maintaining spanning trees in a distributed fashion is central to many networking applications and selfstabilizing algorithms provide an elegant way of doing it in fault-prone environments. In this paper, we propose a self-stabilizing algorithm for maintaining a spanning tree in a distributed fashion for a completely connected topology. Our algorithm requires a node to process O(1) messages on average in one asynchronous round as compared to previous algorithms which need to process messages from every neighbor, resulting in O(n) work in a completely connected topology. Our algorithm also stabilizes faster than the previous approaches. Our approach demonstrates a new methodology which uses the idea of core and non-core states for developing self-stabilizing algorithms. The algorithm is also useful in security related applications due to its unique design.