AbstractIn this paper we consider the problem of finding a spanning k-tree of minimum weight in a complete weighted graph which has a number of applications in designing reliable telecommunication networks. This problem is known to be NP-hard. We propose four effective heuristics: the first heuristic is based on the idea of a well-known Prim's algorithm, the second one is based on a dynamic programming approach, and the other two use the idea of iterative improvement from a starting solution. Preliminary numerical experiment was performed to compare the effectiveness of the proposed algorithms with known heuristics and exact algorithms.