Approximation algorithms for generalized TSP in grid clusters / Khachay M., Neznakhina K. // CEUR Workshop Proceedings. - 2016. - V. 1623, l. . - P. 39-48.

ISSN:
16130073
Type:
Conference Paper
Abstract:
The Generalized Traveling Salesman Problem (GTSP) is a generalization of the well known Traveling Salesman Problem (TSP), where along with a weighted graph G = (V, E, w) we are given by a partition of its node set V = V1 ∪⋯ ∪ Vk into disjunctive subsets or clusters. The goal is to find a minimum cost cycle such that each cluster is hit by exactly one node of this cycle. We consider a geometric setting of the GTSP, in which a partition is specified by cells of the integer 1 × 1 grid (on the Euclidean plane). Even in this special setting, the GTSP remains intractable enclosing the classic Euclidean TSP on the plane. Recently, it was shown that this problem has (1.5+ 8√2+ϵ)-approximation algorithm with complexity bound depending on n and k polynomially, where k is the number of clusters. We propose three approximation algorithms for the Euclidean GTSP on grid clusters. For any fixed k, all proposed algorithms are PTASs. Time complexities of the first two remain polynomial for k = O(logn) while the last one is a PTAS when k = n-O(logn). Copyright © by the paper's authors.
Author keywords:
Approximation algorithm; Generalized traveling salesman; Grid clusters
Index keywords:
Clustering algorithms; Computational complexity; Geometry; Graph theory; Operations research; Optimization; Traveling salesman problem; Complexity bounds; Euclidean planes; Generalized traveling sales
DOI:
нет данных
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Affiliations Krasovskii Institute of Mathematics and Mechanics, Russian Federation; Ural Federal University, Ekaterinburg, Russian Federation; Omsk State Technical University, Omsk, Russian Federation
Author Keywords Approximation algorithm; Generalized traveling salesman; Grid clusters
Funding Details 14-11-00109, RSF, Russian Science Foundation
Funding Text This research was supported by Russian Science Foundation, project no. 14-11-00109.
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Sponsors Far Eastern Federal University, Vladivostok;Higher School of Economics, Nizhny Novgorod;Novosibirsk State University;Russian Foundation for Basic Research
Publisher CEUR-WS
Conference name 9th International Conference on Discrete Optimization and Operations Research, DOOR 2016
Conference date 19 September 2016 through 23 September 2016
Language of Original Document English
Abbreviated Source Title CEUR Workshop Proc.
Source Scopus