Mathematical Programming: Series A and B
Formulations and valid inequalities for the node capacitated graph partitioning problem
Mathematical Programming: Series A and B
Disjunctive programming: properties of the convex hull of feasible points
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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)
On cardinality constrained cycle and path polytopes
Mathematical Programming: Series A and B
Dual consistent systems of linear inequalities and cardinality constrained polytopes
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
The location-dispatching problem: Polyhedral results and content delivery network design
Discrete Applied Mathematics
On cardinality constrained polymatroids
Discrete Applied Mathematics
| Hi-index | 0.00 |
Given a combinatorial optimization problem and a subset N of nonnegative integer numbers, we obtain a cardinality constrained version of this problem by permitting only those feasible solutions whose cardinalities are elements of N. In this paper we briefly touch on questions that address common grounds and differences of the complexity of a combinatorial optimization problem and its cardinality constrained version. Afterwards we focus on the polyhedral aspects of the cardinality constrained combinatorial optimization problems. Maurras (1977) [5] introduced a class of inequalities, called forbidden cardinality inequalities in this paper, that can be added to a given integer programming formulation for a combinatorial optimization problem to obtain one for the cardinality restricted versions of this problem. Since the forbidden cardinality inequalities in their original form are mostly not facet defining for the associated polyhedron, we discuss some possibilities to strengthen them, based on the experiments made in Kaibel and Stephan (2007) and Maurras and Stephan (2009) [2,3].