Forest covers and a polyhedral intersection theorem
Mathematical Programming: Series A and B
Graph minors. IV. Tree-width and well-quasi-ordering
Journal of Combinatorial Theory Series B
The maximal dispersion problem and the “first point outside the neighbourhood” heuristic
Computers and Operations Research
Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
Finding k points with minimum diameter and related problems
Journal of Algorithms
Finding k-cuts within twice the optimal
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Asymptotic analysis of an algorithm for balanced parallel processor scheduling
SIAM Journal on Computing
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
New algorithms for minimum area k-gons
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
On linear time minor tests with depth-first search
Journal of Algorithms
Journal of the ACM (JACM)
Approximation algorithms for geometric tour and network design problems (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
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
Approximation Algorithms for the k-Clique Covering Problem
SIAM Journal on Discrete Mathematics
Discrete Applied Mathematics
The cardinality and precedence constrained maximum value sub-hypergraph problem and its applications
Discrete Applied Mathematics
Theoretical Computer Science - Special issue on computing and combinatorics
Faster geometric k-point MST approximation
Computational Geometry: Theory and Applications
The k-cardinality assignment problem
GO-II Meeting Proceedings of the second international colloquium on Graphs and optimization
A 2.5-factor approximation algorithm for the k-MST problem
Information Processing Letters
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
New Approximation Guarantees for Minimum-Weight k-Trees and Prize-Collecting Salesmen
SIAM Journal on Computing
A Constant-Factor Approximation Algorithm for the Geometric k-MST Problem in the Plane
SIAM Journal on Computing
A constant-factor approximation algorithm for the k-MST problem
Journal of Computer and System Sciences
Finding subsets maximizing minimum structures
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Analysis of Several Task-Scheduling Algorithms for a Model of Multiprogramming Computer Systems
Journal of the ACM (JACM)
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Fast algorithms for k-shredders and k-node connectivity augmentation
Journal of Algorithms
A 2 + ε approximation algorithm for the k-MST problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for dispersion problems
Journal of Algorithms
Efficient algorithms and codes for (italic)k(/italic)-cardinality assignment problems
Discrete Applied Mathematics
Approximation algorithms for maximization problems arising in graph partitioning
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Decomposing Matrices into Blocks
SIAM Journal on Optimization
Genetic Algorithm and Graph Partitioning
IEEE Transactions on Computers
Greedily Finding a Dense Subgraph
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
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
On the densest k-subgraph problems
On the densest k-subgraph problems
Approximation schemes for Metric Bisection and partitioning
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Cardinality constrained minimum cut problems: complexity and algorithms
Discrete Applied Mathematics
Variable neighborhood decomposition search for the edge weighted k-cardinality tree problem
Computers and Operations Research
Heuristic Algorithms and Scatter Search for the Cardinality Constrained P|Cmax Problem
Journal of Heuristics
New metaheuristic approaches for the edge-weighted k-cardinality tree problem
Computers and Operations Research
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
On-Line Algorithms for Cardinality Constrained Bin Packing Problems
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Lower bounds for the partitioning of graphs
IBM Journal of Research and Development
On uniform k-partition problems
Discrete Applied Mathematics
Hybrid rounding techniques for knapsack problems
Discrete Applied Mathematics - Special issue: Efficient algorithms
On bounds for the k-partitioning of graphs
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Lot-sizing polyhedra with a cardinality constraint
Operations Research Letters
Lexicographic bottleneck problems
Operations Research Letters
A two-phase local search for the K clusters with fixed cardinality problem
MACMESE'10 Proceedings of the 12th WSEAS international conference on Mathematical and computational methods in science and engineering
Approximating minimum cut with bounded size
INOC'11 Proceedings of the 5th international conference on Network optimization
Symmetry matters for the sizes of extended formulations
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Cardinality constrained combinatorial optimization: Complexity and polyhedra
Discrete Optimization
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In this paper, we consider combinatorial optimization problems with additional cardinality constraints. In k-cardinality combinatorial optimization problems, a cardinality constraint requires feasible solutions to contain exactly k elements of a finite set E. Problems of this type have applications in many areas, e.g. in the mining and oil industry, telecommunications, circuit layout, and location planning. We formally define the problem, mention some examples and summarize general results. We provide an annotated bibliography of combinatorial optimization problems of which versions with cardinality constraint have been considered in the literature.