A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Spanning Trees---Short or Small
SIAM Journal on Discrete Mathematics
A constant-factor approximation algorithm for the k MST problem (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A 2 + ε approximation algorithm for the k-MST problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximate k-MSTs and k-Steiner Trees via the Primal-Dual Method and Lagrangean Relaxation
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Local search algorithms for the k-cardinality tree problem
Discrete Applied Mathematics
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Variable neighborhood decomposition search for the edge weighted k-cardinality tree problem
Computers and Operations Research
Saving an epsilon: a 2-approximation for the k-MST problem in graphs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
A new hybrid evolutionary algorithm for the huge k-cardinality tree problem
Proceedings of the 8th annual conference on Genetic and evolutionary computation
New metaheuristic approaches for the edge-weighted k-cardinality tree problem
Computers and Operations Research
Strong Formulations for 2-Node-Connected Steiner Network Problems
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
A new ILP formulation for 2-root-connected prize-collecting Steiner networks
ESA'07 Proceedings of the 15th annual European conference on Algorithms
IWANN'05 Proceedings of the 8th international conference on Artificial Neural Networks: computational Intelligence and Bioinspired Systems
Reconstructing geometrically consistent tree structures from noisy images
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part I
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Given an undirected graph G = (V,E) with edge weights and a positive integer number k, the k-cardinality tree problem consists of finding a subtree T of G with exactly k edges and the minimum possible weight. Many algorithms have been proposed to solve this NP-hard problem, resulting in mainly heuristic and metaheuristic approaches. In this article, we present an exact ILP-based algorithm using directed cuts. We mathematically compare the strength of our formulation to the previously known ILP formulations of this problem, and show the advantages of our approach. Afterwards, we give an extensive study on the algorithm's practical performance compared to the state-of-the-art metaheuristics. In contrast to the widespread assumption that such a problem cannot be efficiently tackled by exact algorithms for medium and large graphs (between 200 and 5,000 nodes), our results show that our algorithm not only has the advantage of proving the optimality of the computed solution, but also often outperforms the metaheuristic approaches in terms of running time.