Counting Unique-Sink Orientations
Jan Foniok, Bernd G\"artner, Lorenz Klaus, Markus Sprecher
TL;DR
This paper studies unique-sink orientations of the n-cube graph, providing bounds and characterizations relevant to the linear complementarity problem and K-matrices.
Contribution
It offers new bounds on classes of USOs and characterizes K-matrices through their associated USOs, advancing understanding in combinatorial optimization.
Findings
Established new lower and upper bounds for USO classes
Characterized K-matrices via USO properties
Connected USOs to the linear complementarity problem
Abstract
Unique-sink orientations (USOs) are an abstract class of orientations of the n-cube graph. We consider some classes of USOs that are of interest in connection with the linear complementarity problem. We summarise old and show new lower and upper bounds on the sizes of some such classes. Furthermore, we provide a characterisation of K-matrices in terms of their corresponding USOs.
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