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

• Published in: Learning and Intelligent Optimization Vol. 11353; pp. 441 - 446
• Main Authors: Khachay, Michael, Neznakhina, Katherine
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2019; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Generalized traveling salesman problem; Polynomial time solvability; Pseudo-pyramidal tour
• ISBN: 3030053474; 9783030053475
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-05348-2_38

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.