Cardinality constrained minimum cut problems: complexity and algorithms

Authors:
Maurizio Bruglieri;Francesco Maffioli;Matthias Ehrgott
Affiliations:
Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy;Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy;Department of Engineering Science, University of Auckland, Private Bag 92019, Auckland, New Zealand
Venue:
Discrete Applied Mathematics
Year:
2004

Citing 12
Cited 5

Constructing a perfect matching is in random NC

Combinatorica
An application of combinatorial optimization to statistical physics and circuit layout design

Operations Research
An efficient algorithm for the minimum capacity cut problem

Mathematical Programming: Series A and B
Finding k-cuts within twice the optimal

SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
On the computation of Pfaffians

Discrete Applied Mathematics
Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

Journal of the ACM (JACM)
Semidefinite programming in combinatorial optimization

Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
A simple min-cut algorithm

Journal of the ACM (JACM)
The k-cardinality assignment problem

GO-II Meeting Proceedings of the second international colloquium on Graphs and optimization
Fast Probabilistic Algorithms for Verification of Polynomial Identities

Journal of the ACM (JACM)
Heuristics for cardinality constrained portfolio optimisation

Computers and Operations Research
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)
Approximation algorithms for the bi-criteria weighted MAX-CUT problem

Discrete Applied Mathematics
Cardinality constrained and multicriteria (multi)cut problems

Journal of Discrete Algorithms
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)
Multicriteria global minimum cuts

ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation

Quantified Score

Hi-index	0.04

Visualization

Abstract

In several applications the solutions of combinatorial optimization problems (COP) are required to satisfy an additional cardinality constraint, that is to contain a fixed number of elements. So far the family of (COP) with cardinality constraints has been little investigated. The present work tackles a new problem of this class: the k-cardinality minimum cut problem (k-card cut). For a number of variants of this problem we show complexity results in the most significant graph classes. Moreover, we develop several heuristic algorithms for the k-card cut problem for complete, complete bipartite, and general graphs. Lower bounds are obtained through an SDP formulation, and used to show the quality of the heuristics. Finally, we present a randomized SDP heuristic and numerical results.