An Optimal Minimum Spanning Tree Algorithm
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
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We present a deterministic algorithm to find a minimum spanning forest of an edge-weighted undirected graph. On a graph with n vertices and m edges, the algorithm runs in time O(T^*(m,n)) where T^* is the decision-tree complexity of the problem. This time bound is provably optimal as a function of n and m. The algorithm is quite simple, and can be implemented on a pointer machine. The exact function describing the running time of our algorithm is not known at present. The current best bounds known for T^* (and hence the running time of our algorithm) are that T^*(m,n) is at least linear in m, and T^*(m,n) = O(m alpha (m,n) log alpha (m,n)), where alpha, a certain natural inverse of Ackermann''s function, is an extremely slow-growing function.