Variable neighborhood decomposition search for the edge weighted k-cardinality tree problem

The minimum k-cardinality tree problem on graph G consists in finding a subtree of G with exactly k edges whose sum of weights is minimum. A number of heuristic methods have been developed recently to solve this NP-hard problem. In this paper a decomposition approach is developed and implemented within a successive approximation scheme known as variable neighborhood decomposition search. This approach obtains superior results over existing methods, and furthermore, allows larger problem instances (up to 5000 nodes) to be solved more efficiently.