Abstract: This paper provides a method of producing a minimum cost spanning tree (MCST) using set operations. It studies the data structure for implementation of set operations and the algorithm to be applied to this structure and proves tile correctness and the complexity of the algorithm. This algorithm uses the FDG (formula to divide elements into groups) to sort (the FDG sorts a sequence of n elements in expected lim O(n)) and uses the method of path compression to find and to unite. Therefore, it produces an MCST of an undirected network having n vertices and e edges in expected time O(eG(n)).

Key words: Minimum cost spanning tree, A sort using the FDG, Path compression, Set operation of find and unite, Algorithm analysis