Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1141589 | Discrete Optimization | 2009 | 14 Pages |
Abstract
In this paper we study the structure of the kk-assignment polytope, whose vertices are the m×nm×n (0, 1)-matrices with exactly kk 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Control and Optimization
Authors
Jonna Gill, Svante Linusson,