Year: 2017
Type: preprint
Abstract: In the study of extensions of polytopes of combinatorial optimization problems, a notorious open question is that for the size of the smallest extended formulation of the Minimum Spanning Tree problem on a complete graph with $n$ nodes. The best known lower bound is $Ω(n^2)$, the best known upper bound is $O(n^3)$. In this note we show that the venerable fooling set method cannot be used to improve the lower bound: every fooling set for the Spanning Tree polytope has size $O(n^2)$.
Source: arXiv (Cornell University)
Authors: Khoshkhah, Kaveh, Theis, Dirk Oliver
Institution: University of Tartu
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949912126