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On the Nearest-Neighbor Algorithm for the Mean-Field Traveling Salesman Problem

Part of: Graph theory Special processes Theory of computing Algorithms - Computer Science

Published online by Cambridge University Press:  30 January 2018

Antar Bandyopadhyay  and
Farkhondeh Sajadi
Antar Bandyopadhyay*
Affiliation:
Indian Statistical Institute, Delhi and Kolkata
Farkhondeh Sajadi*
Affiliation:
Indian Statistical Institute, Delhi
*
∗ Postal address: Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Delhi Centre, 7 S. J. S. Sansanwal Marg, New Delhi, 110016, India.
∗ Postal address: Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Delhi Centre, 7 S. J. S. Sansanwal Marg, New Delhi, 110016, India.
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Abstract

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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.

Keywords

Nearest-neighbor algorithmmean-field setuptraveling salesman problem

MSC classification

Primary: 60K37: Processes in random environments
Secondary: 05C85: Graph algorithms 68Q87: Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) 68W25: Approximation algorithms
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 1 , March 2014 , pp. 106 - 117
Copyright
© Applied Probability Trust 

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