Publication Date:
2022-03-11
Description:
In this thesis we investigate the hyperassignment problem with a special focus on
connections to the theory of hypergraphs, in particular balanced and normal hyper-
graphs, as well as its relation to the Stable Set Problem.
The main point is the investigation of the matching and perfect matching polytope for partitioned hypergraphs. Therefore, valid inequalities, facets,
and the dimension of some polytopes are given. Furthermore, we show that the trivial LP-relaxation of the Hyperassignment Problem obtained by relaxing x_i ∈ {0, 1}
by 0 ≤ x_i ≤ 1 has an arbitrarily large integrality gap, even after adding all clique inequalities. Whereas the integrality gap of the trivial LP-relaxation of the maximum weight
matching problem for partitioned hypergraphs with maximum part size M is at most
2M − 1.
Additionally, computational results for small partitioned hypergraphs of part size
two are presented. Using symmetry it was possible to calculate all minimal fractional vertices
of the fractional perfect matching polytope of partitioned hypergraphs with part size
two having at most twelve vertices.
Language:
English
Type:
masterthesis
,
doc-type:masterThesis
Format:
application/pdf
