An O(|E| log log |V|) Algorithm for Finding Minimum Spanning Trees

best MST algorithms known have running time O(lEl X lo$ Vi) for sparse graphs [I 1, aad more recently Tarjan iii21 has an algorithm that iequires O(IE1 x\ oglVl)time.’ Our algorithm is a modification of an algorithm by SoWn [3]. His method works by successively enlarging , components al the MST. In the frost stage the minimum-cost edge incident upon each node of G is fcdnd. These edges arc part of the MST sought. The croups of vertices that are connected by these edges are then identified. By shrinking each such group of vertices to node, we obtain a new graph with at most odes. This process is repeated for a number of for a new graph, until finally 8 s@le contracted node remains. Clearly each stage of elves O(I&j) operations, and logs VI