Subtour Elimination Constraints Imply a Matrix-Tree Theorem SDP Constraint for the TSP
Discrete Mathematics
2019-07-29 v1 Data Structures and Algorithms
Optimization and Control
Abstract
De Klerk, Pasechnik, and Sotirov give a semidefinite programming constraint for the Traveling Salesman Problem (TSP) based on the matrix-tree Theorem. This constraint says that the aggregate weight of all spanning trees in a solution to a TSP relaxation is at least that of a cycle graph. In this note, we show that the semidefinite constraint holds for any weighted 2-edge-connected graph and, in particular, is implied by the subtour elimination constraints of the subtour elimination linear program. Hence, this semidefinite constraint is implied by a finite set of linear inequality constraints.
Keywords
Cite
@article{arxiv.1907.11669,
title = {Subtour Elimination Constraints Imply a Matrix-Tree Theorem SDP Constraint for the TSP},
author = {Samuel C. Gutekunst and David P. Williamson},
journal= {arXiv preprint arXiv:1907.11669},
year = {2019}
}