Many fundamental combinatorial problems exhibit characteristic structures. Such properties can be exploited for deriving efficient algorithms and, moreover, are often helpful for solving general integer programs with binary variables. A good example are the various known inequalities for the stable set polytope.

The investigation of integer generalizations of such basic problems aims at the identification of similar structures and their application for solving general integer programs. In this project, we in particular study stable multi-sets as an appropriate extension of stable sets.

## StableMultiSets

### Integer generalizations of basic 0-1 problems

Many fundamental combinatorial problems exhibit characteristic structures. Such properties can be exploited for deriving efficient algorithms and, moreover, are often helpful for solving general integer programs with binary variables. A good example are the various known inequalities for the stable set polytope. The investigation of integer generalizations of such basic problems aims at the identification of similar structures and their application for solving general integer programs. In this project, we in particular study stable multi-sets as an appropriate extension of stable sets.

### Description

### Project objective

### Publications

- A. M. C. A. Koster, A. Zymolka.
**On cycles and the stable multi-set polytope**.*Discrete Optimization, 2(3):241–255, 2005*.