Journal of Applied Probability

On the nearest-neighbor algorithm for the mean-field traveling salesman problem

Antar Bandyopadhyay and Farkhondeh Sajadi

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Abstract

In this work we consider the mean-field traveling salesman problem, where the intercity distances are taken to be independent and identically distributed with some distribution F. We consider the simplest approximation algorithm, namely, the nearest-neighbor algorithm, where the rule is to move to the nearest nonvisited city. We show that the limiting behavior of the total length of the nearest-neighbor tour depends on the scaling properties of the density of F at 0 and derive the limits for all possible cases of general F.

Article information

Source
J. Appl. Probab. Volume 51, Number 1 (2014), 106-117.

Dates
First available in Project Euclid: 25 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1395771417

Digital Object Identifier
doi:10.1239/jap/1395771417

Mathematical Reviews number (MathSciNet)
MR3189445

Zentralblatt MATH identifier
1321.90114

Subjects
Primary: 60K37: Processes in random environments
Secondary: 05C85: Graph algorithms [See also 68R10, 68W05] 68Q87: Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) [See also 68W20, 68W40] 68W25: Approximation algorithms

Keywords
Nearest-neighbor algorithm mean-field setup traveling salesman problem

Citation

Bandyopadhyay, Antar; Sajadi, Farkhondeh. On the nearest-neighbor algorithm for the mean-field traveling salesman problem. J. Appl. Probab. 51 (2014), no. 1, 106--117. doi:10.1239/jap/1395771417. https://projecteuclid.org/euclid.jap/1395771417.


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