## Journal of Applied Probability

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

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

Antar Bandyopadhyay and Farkhondeh Sajadi

#### 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