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Maintaining spanning trees in a distributed fashion is central to many networking applications. 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 of size O(log n) on average in one cycle 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.

Distributed Maintenance of a Spanning Tree Using Labeled Tree Encoding