OFFLINE ALGORITHMS FOR DYNAMIC MINIMUM SPANNING TREE PROBLEMS

We describe an efficient algorithm for maintaining a minimum spanning tree (MST) in a graph subject to a sequence of edge weight modifications. The sequence of minimum spanning trees is computed offline, after the sequence of modifications is known. The algorithm takes time O(k log n) for a sequence of k updates to a graph of n vertices, giving a bound of O(log n) on the average time per update. We use our techniques to solve the offline geometric MST problem for a planar point set subject to insertions and deletions; our algorithm for this problem takes time O(k log(2) n), for an average of O(log(2) n) time per update. We describe a further refinement of our technique which solves the problem in the rectilinear metric in time O(k log n log log n), for an average of O(log n log log n) time per update. (C) 1994 Academic Press, Inc.