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The minimum spanning tree (MST) construction is a classical problem in Distributed Computing for creating a globally minimized structure distributedly. Self-stabilization is versatile technique for forward recovery that permits to handle any kind of transient faults in a unified manner. The loop-free property provides interesting safety assurance in dynamic networks where edge-cost changes during operation of the protocol.We present a new self-stabilizing MST protocol that improves on previous known approaches in several ways. First, it makes fewer system hypotheses as the size of the network (or an upper bound on the size) need not be known to the participants. Secondly, it is loop-free in the sense that it guarantees that a spanning tree structure is always preserved while edge costs change dynamically and the protocol adjusts to a new MST. Finally, time complexity matches the best known results, while space complexity results show that this protocol is the most efficient to date. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the connection, by a provider, of multiple groups of nodes spread over a network. The role of the provider is to interconnect the members of every group. For this purpose, it must distribute the available links of the network between the groups. The general aim then is to allocate these links in such a way that the communications latencies in the allocated structure are equivalent to the ones in the original (full) network for each group. We study two approaches constructing structures preserving the maximum latency (called the diameter). Unfortunately we show that the associated optimization graph problems are difficult (one cannot be approximated by a constant and the other is NP-complete). Due to these difficulties we relax the constraint on the diameter and propose to construct a unique tree connecting all the groups together. We give a heuristic to treat this problem and we propose several analytical results on its maximum and average latencies performance. [ABSTRACT FROM PUBLISHER]