Traveling Salesman Algorithms Complexity

Labeled Traveling Salesman Problems: Complexity and approximation

We consider labeled Traveling Salesman Problems, defined upon a complete graph of n vertices with colored edges. The objective is to find a tour of maximum (or minimum) number of colors. We derive results regarding hardness of approximation and analyze approximation algorithms, for both versions of the problem. For the maximization version we give a 1 2 -approximation algorithm based on local i...

Genetic Algorithms for the Traveling Salesman Problem

This paper is a survey of genetic algorithms for t h e traveling salesman problem. Genetic algorithms are randomized search techniques that simulate some of the processes observed i n natural evolution. In this paper, a simple genetic algorithm is introduced, and various extensions are presented to solve t h e traveling salesman problem. Computational results are also repor ted for both random ...

Genetic Algorithms and the Traveling Salesman

Generalized Traveling Salesman Problem Reduction Algorithms

The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The aim of this paper is to present a problem reduction algorithm that deletes redundant vertices and edges, preserving the value o...

Approximation algorithms for the traveling salesman problem

We first prove that the minimum and maximum traveling salesman problems, their metric versions as well as some versions defined on parameterized triangle inequalities (called sharpened and relaxed metric traveling salesman) are all equi-approximable under an approximation measure, called differential-approximation ratio, that measures how the value of an approximate solution is placed in the in...