A [formula omitted]-approximation algorithm for the clustered traveling salesman tour and path problems

We consider the ordered cluster traveling salesman problem (OCTSP). In this problem, a vehicle starting and ending at a given depot must visit a set of n points. The points are partitioned into K, K⩽n , prespecified clusters. The vehicle must first visit the points in cluster 1, then the points in c...

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Bibliographic Details
Published in:Operations research letters Vol. 24; no. 1; pp. 29 - 35
Main Authors: Anily, Shoshana, Bramel, Julien, Hertz, Alain
Format: Journal Article
Language:English
Published: Elsevier B.V 01.02.1999
Subjects:
Analysis of algorithms
Suboptimal algorithms
Transportation
Vehicle routing
Suboptimal algorithms
Analysis of algorithms
Vehicle routing
Transportation
ISSN:0167-6377, 1872-7468
Online Access:Get full text
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Summary:We consider the ordered cluster traveling salesman problem (OCTSP). In this problem, a vehicle starting and ending at a given depot must visit a set of n points. The points are partitioned into K, K⩽n , prespecified clusters. The vehicle must first visit the points in cluster 1, then the points in cluster 2,… , and finally the points in cluster K so that the distance traveled is minimized. We present a 5 3 -approximation algorithm for this problem which runs in O( n 3) time. We show that our algorithm can also be applied to the path version of the OCTSP: the ordered cluster traveling salesman path problem (OCTSPP). Here the (different) starting and ending points of the vehicle may or may not be prespecified. For this problem, our algorithm is also a 5 3 -approximation algorithm.
ISSN:0167-6377
1872-7468
DOI:10.1016/S0167-6377(98)00046-7