The k-assignment polytope

Authors:
Jonna Gill;Svante Linusson
Affiliations:
Matematiska Institutionen, Linköpings Universitet, 581 83 Linköping, Sweden;Matematiska Institutionen, Royal Institute of Technology (KTH), SE-100 44, Stockholm, Sweden
Venue:
Discrete Optimization
Year:
2009

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Abstract

In this paper we study the structure of the k-assignment polytope, whose vertices are the mxn (0, 1)-matrices with exactly k 1:s and at most one 1 in each row and each column. This is a natural generalisation of the Birkhoff polytope and many of the known properties of the Birkhoff polytope are generalised. A representation of the faces by certain bipartite graphs is given. This tool is used to describe the properties of the polytope, especially a complete description of the cover relation in the face poset of the polytope and an exact expression for the diameter. An ear decomposition of these bipartite graphs is constructed.