Abstract
This paper considers the Updating Minimum-weight Spanning Tree Problem (UMP), that is, the problem to update the Minimum-weight Spanning Tree (MST) in response to topology change of the network. This paper proposes the algorithm which reconstructs the MST after several links are deleted and added. Its message complexity and its ideal-time complexity are O(m+n log (t+f)) and O(n+n log(t+f)) respectively, where n is the number of processors in the network, t (resp. f) is the number of added links (resp. the number of deleted links of the old MST), and m=t+n if f=0, m=e (i.e. the number of links in the network after the topology change) otherwise. The last part of this paper touches on the algorithm which deals with deletion and addition of processors as well as links.
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