An Optimal Minimum Spanning Tree Algorithm

We establish that the algorithmic complexity of the minimum spanning tree problem is equal to its decision-tree complexity. Specifically, we present a deterministic algorithm to find a minimum spanning tree of a graph with n vertices and m edges that runs in time O(T (m, n)) where T is the minimum number of edge-weight comparisons needed to determine the solution. The algorithm is quite simple and can be implemented on a pointer machine. Although our time bound is optimal, the exact function describing it is not known at present. The current best bounds known for T are T (m, n) = (m) and T (m, n) = O(m

• Type: Conference
• Year: 2000
• Where: ICALP
• Authors: Seth Pettie, Vijaya Ramachandran
• Keywords: Algorithms, ICALP 2000, Minimum Spanning Tree, Programming Languages, Spanning Tree Problem