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arXiv · 1907.11669

Subtour Elimination Constraints Imply a Matrix-Tree Theorem SDP Constraint for the TSP

Samuel C. Gutekunst·David P. Williamson
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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.

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Samuel C. Gutekunst, David P. Williamson. 2019-07-26. Subtour Elimination Constraints Imply a Matrix-Tree Theorem SDP Constraint for the TSP. https://arxiv.org/abs/1907.11669

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