An annotated bibliography of combinatorial optimization problems with fixed cardinality constraints

Authors:
Maurizio Bruglieri;Matthias Ehrgott;Horst W. Hamacher;Francesco Maffioli
Affiliations:
Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milano, Italy;Department of Engineering Science, The University of Auckland, Auckland, New Zealand;Fachbereich Mathematik, Universität Kaiserslautern, Kaiserslautern, Germany;Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milano, Italy
Venue:
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
Year:
2006

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Abstract

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.