The traveling salesman problem in graphs with 3-edge cutsets-Reference-Cited by-同舟云学术

The traveling salesman problem in graphs with 3-edge cutsets

Published:1985-04 Issue:2 Volume:32 Page:383-410
ISSN:0004-5411
Container-title:Journal of the ACM
language:en
Short-container-title:J. ACM

Author:

Cornuéjols G.¹,Naddef D.²,Pulleyblank W.³

Affiliation:

1. Carnegie-Mellon Univ., Pittsburgh, PA

2. Univ. Scientifique et Me´dicale and Univ. des Sci. Sociales, Grenoble, France

3. Univ. of Waterloo, Waterloo, Ont., Canada

Abstract

This paper analyzes decomposition properties of a graph that, when they occur, permit a polynomial solution of the traveling salesman problem and a description of the traveling salesman polytope by a system of linear equalities and inequalities. The central notion is that of a 3-edge cutset, namely, a set of 3 edges that, when removed, disconnects the graph. Conversely, our approach can be used to construct classes of graphs for which there exists a polynomial algorithm for the traveling salesman problem. The approach is illustrated on two examples, Halin graphs and prismatic graphs.

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Link

https://dl.acm.org/doi/pdf/10.1145/3149.3154

Reference31 articles.

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4. Solving large-scale symmetric travelling salesman problems to optimality;CROWDER H.;Manage. Sci.,1980

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