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Pseudo-pyramidal Tours and Efficient Solvability of the Euclidean Generalized Traveling Salesman Problem in Grid Clusters

  • Michael Khachay
  • Katherine Neznakhina
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11353)

Abstract

Generalized Traveling Salesman Problem (GTSP) is a well-known combinatorial optimization problem having numerous applications in operations research. For a given edge-weighted graph and a partition of its nodeset onto k (disjoint) clusters it is required to find a minimum cost cyclic tour visiting all the clusters once. The problem is strongly NP-hard even in the Euclidean plane provided the number of clusters is a part of the instance. Recently we proposed efficient optimal algorithms for GTSP based on quasi- and pseudo-pyramidal tours. As a consequence, we proved polynomial time solvability of the Euclidean GTSP in Grid Clusters defined by a grid of height at most 2. In this short paper, we show how to extend this result to the case defined by grids of an arbitrary fixed height.

Keywords

Generalized traveling salesman problem Pseudo-pyramidal tour Polynomial time solvability 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Krasovsky Institute of Mathematics and MechanicsEkaterinburgRussia
  2. 2.Ural Federal UniversityEkaterinburgRussia
  3. 3.Omsk State Technical UniversityOmskRussia

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