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Polynomial Time Solvable Subclass of the Generalized Traveling Salesman Problem on Grid Clusters

  • Michael KhachayEmail author
  • Katherine Neznakhina
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10716)

Abstract

The Generalized Traveling Salesman Problem on Grid Clusters (GTSP-GC) is the geometric setting of the famous Generalized Traveling Salesman Problem, where the nodes of a given graph are points on the Euclidean plane and the clusters are defined implicitly by the cells of a unit grid. The problem in question is strongly NP-hard but can be approximated in polynomial time with a fixed ratio. In this paper we describe a new non-trivial polynomially solvable subclass of GTSP-GC. Providing new min-max guarantee for the optimal clustering loss in one-dimensional 2-medians problem, we show that any instance of this subclass has a quasi-pyramidal optimal route, which can be found by dynamic programming in polynomial time.

Keywords

Generalized traveling salesman Grid clusters Pyramidal tour 

Notes

Acknowledgments

This research was supported by Russian Science Foundation, project no. 14-11-00109.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Krasovsky Institute of Mathematics and MechanicsUral Federal UniversityEkaterinburgRussia
  2. 2.Omsk State Technical UniversityOmskRussia

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