Parallel algorithms for verification and sensitivity analysis of minimum spanning trees

To verify whether a spanning tree T(V,E) of graph G(V,E´) is a minimum spanning tree, two parallel algorithms are presented. The first algorithm requires O(log n) time and O(max{m/log n, n^3/2/log n}) processors, where |E´|=m and |V|=n. The second algorithm requires O(log n) time and O(m) processors or O(log nloglog n) time and O(max{m/log n, n}) processors. The first algorithm is optimal when G is dense, compared with its O(m) time sequential version. The second algorithm has better performance when G is sparse. By using above results, we also present an efficient algorithm for sensitivity analysis of minimum spanning trees which requires O(log n) time and O(max{m, n ²/log n}) processors. All proposed algorithms in this paper are based on the parallel computational model called CREW PRAM