Layers and matroids for the traveling salesman’s paths

Gottschalk and Vygen proved that every solution of the subtour elimination linear program for traveling salesman paths is a convex combination of more and more restrictive “generalized Gao-trees”. We give a short proof of this fact, as a layered convex combination of bases of a sequence of increasin...

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Bibliographic Details
Published in:Operations research letters Vol. 46; no. 1; pp. 60 - 63
Main Authors: Schalekamp, Frans, Sebő, András, Traub, Vera, van Zuylen, Anke
Format: Journal Article
Language:English
Published: Elsevier B.V 01.01.2018
Elsevier
Subjects:
Approximation algorithm
Christofides’ heuristic
Combinatorics
Computer Science
Discrete Mathematics
Mathematics
Matroid partition
Path traveling salesman problem (TSP)
Polyhedra
Spanning tree
Christofides’ heuristic
Polyhedra
Matroid partition
Approximation algorithm
Path traveling salesman problem (TSP)
Spanning tree
ISSN:0167-6377, 1872-7468
Online Access:Get full text
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Summary:Gottschalk and Vygen proved that every solution of the subtour elimination linear program for traveling salesman paths is a convex combination of more and more restrictive “generalized Gao-trees”. We give a short proof of this fact, as a layered convex combination of bases of a sequence of increasingly restrictive matroids. A strongly polynomial, combinatorial algorithm follows for finding this convex combination, which is a new tool offering polyhedral insight, already instrumental in recent results for the s−t path TSP.
ISSN:0167-6377
1872-7468
DOI:10.1016/j.orl.2017.11.002