Improved approximation guarantees for minimum-weight k-trees and prize-collecting salesmen
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
A constant-factor approximation for the k-MST problem in the plane
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Spanning Trees---Short or Small
SIAM Journal on Discrete Mathematics
Faster geometric k-point MST approximation
Computational Geometry: Theory and Applications
New Approximation Guarantees for Minimum-Weight k-Trees and Prize-Collecting Salesmen
SIAM Journal on Computing
A constant-factor approximation algorithm for the k-MST problem
Journal of Computer and System Sciences
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
Solution of the Cumulative Assignment Problem With a Well-Structured TabuSearch Method
Journal of Heuristics
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Information Processing Letters
A new hybrid evolutionary algorithm for the huge k-cardinality tree problem
Proceedings of the 8th annual conference on Genetic and evolutionary computation
An annotated bibliography of combinatorial optimization problems with fixed cardinality constraints
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
New metaheuristic approaches for the edge-weighted k-cardinality tree problem
Computers and Operations Research
The prize collecting Steiner tree problem: models and Lagrangian dual optimization approaches
Computational Optimization and Applications
Local and variable neighborhood search for the k-cardinality subgraph problem
Journal of Heuristics
Obtaining optimal k-cardinality trees fast
Journal of Experimental Algorithmics (JEA)
An annotated bibliography of combinatorial optimization problems with fixed cardinality constraints
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
The k-Cardinality Tree Problem: Reformulations and Lagrangian Relaxation
Discrete Applied Mathematics
IWANN'05 Proceedings of the 8th international conference on Artificial Neural Networks: computational Intelligence and Bioinspired Systems
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In this paper we deal with an NP-hard combinatorial optimization problem, the k-cardinality tree problem in node-weighted graphs. This problem has several applications, which justify the need for efficient methods to obtain good solutions. We review existing literature on the problem. Then we prove that under the condition that the graph contains exactly one trough, the problem can be solved in polynomial time. For the general NP-hard problem we implemented several local search methods to obtain heuristic solutions, which are qualitatively better than solutions found by constructive heuristics and which require significantly less time than needed to obtain optimal solutions. We used the well-known concepts of genetic algorithms and tabu search with useful extensions. The general performance of our methods is illustrated by numerical results.