A parallel algorithm for multiple edge updates of minimum spanning trees

The authors present a parallel algorithm for the multiple edge update problem on a minimum spanning tree. This problem is defined as follows: given a minimum spanning tree T(V,E/sub T/) of an undirected graph G(V,E), where mod V mod =n and E/sub T/ is the set of tree edges, recompute a new minimum spanning tree when (1) adding K new edges, (2) changing the weights of existent K edges, or (3) deleting a vertex of degree K in the tree, where 1<or=K<n. Their algorithm requires O(logKlogn) time and O(n/sup 2//lognlogK) processors on a SIMD CREW PRAM model. If the weights of the current tree edges are not allowed to increase, then their algorithm runs in the same time bound, but only using O(max(n,nK/lognlogK)) processors. Their algorithm is optimal for dense graphs, if no intermediate results are available from computing the original MST.<<ETX>>

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