Abstract
Abstract Given an undirected graph, the k -cardinality tree problem (KCTP) is the problem of finding a subtree with exactly k edges whose sum of weights is minimum. In this paper we present a lower bound for KCTP based on the work by Kataoka et al. [Kataoka, S., N. Araki and T. Yamada, Upper and lower bounding procedures for the minimum rooted k -subtree problem, European Journal of Operational Research, 122 (2000), 561–569]. This new bound is the basis for the development of a branch-and-bound algorithm for the problem. Experiments carried out on instances from KCTLib revealed that the new exact algorithm largely outperforms the previous approach.
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