Self-stabilizing minimum-degree spanning tree within one from the optimal degree

Lélia Blin (1, 2) , Maria Gradinariu Potop-Butucaru (3) , Stephane Rovedakis (1)

1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes
2 NPA - Networks and Performance Analysis
3 Regal - Large-Scale Distributed Systems and Applications

We propose a self-stabilizing algorithm for constructing a Minimum-Degree Spanning Tree (MDST) in undirected networks. Starting from an arbitrary state, our algorithm is guaranteed to converge to a legitimate state describing a spanning tree whose maximum node degree is at most ∆∗ + 1, where ∆∗ is the minimum possible maximum degree of a spanning tree of the network. To the best of our knowledge our algorithm is the first self stabilizing solution for the construction of a minimum-degree spanning tree in undirected graphs. The algorithm uses only local communications (nodes interact only with the neighbors at one hop distance). Moreover, the algorithm is designed to work in any asynchronous message passing network with reliable FIFO channels. Additionally, we use a fine grained atomicity model (i.e. the send/receive atomicity). The time complexity of our solution is O(mn2 log n) where m is the number of edges and n is the number of nodes. The memory complexity is O(δ log n) in the send-receive atomicity model (δ is the maximal degree of the network).

Domaines: Algorithme et structure de données [cs.DS]

Lélia Blin, Maria Gradinariu Potop-Butucaru, Stephane Rovedakis. Self-stabilizing minimum-degree spanning tree within one from the optimal degree. 23rd IEEE International Symposium on Parallel&Distributed Processing (IPDPS 2009), May 2009, Rome, Italy. pp.1-11, ⟨10.1109/IPDPS.2009.5161042⟩. ⟨inria-00336713⟩