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The adjacency relation on the traveling salesman polytope is NP-Complete

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Abstract

We consider the problem of determining whether two traveling salesman tours correspond to non-adjacent vertices of the convex polytope associated with the traveling salesman problem. This problem is shown to be NP-Complete for both the symmetric and nonsymmetric traveling salesman problem. Several implications are discussed.

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Authors and Affiliations

  1. Harvard University, Cambridge, MA, USA

    Christos H. Papadimitriou

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  1. Christos H. Papadimitriou
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Additional information

This Research was supported by NSF Grant GK-420488, the U.S. Army Research Office-Durham under Grant DAHC04-75-G0192, and an IBM Fellowship.

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Papadimitriou, C.H. The adjacency relation on the traveling salesman polytope is NP-Complete. Mathematical Programming 14, 312–324 (1978). https://doi.org/10.1007/BF01588973

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  • DOI: https://doi.org/10.1007/BF01588973

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