Approximation Algorithms for MultiCriteria Traveling Salesman Problems
Abstract
In multicriteria optimization problems, several objective functions have to be optimized. Since the different objective functions are usually in conflict with each other, one cannot consider only one particular solution as the optimal solution. Instead, the aim is to compute a socalled Pareto curve of solutions. Since Pareto curves cannot be computed efficiently in general, we have to be content with approximations to them. We design a deterministic polynomialtime algorithm for multicriteria gmetric STSP that computes (min{1 +g, 2g^2/(2g^2 2g +1)} + eps)approximate Pareto curves for all 1/2<=g<=1. In particular, we obtain a (2+eps)approximation for multicriteria metric STSP. We also present two randomized approximation algorithms for multicriteria gmetric STSP that achieve approximation ratios of (2g^3 +2g^2)/(3g^2 2g +1) + eps and (1 +g)/(1 +3g 4g^2) + eps, respectively. Moreover, we present randomized approximation algorithms for multicriteria gmetric ATSP (ratio 1/2 + g^3/(1 3g^2) + eps) for g < 1/sqrt(3)), STSP with weights 1 and 2 (ratio 4/3) and ATSP with weights 1 and 2 (ratio 3/2). To do this, we design randomized approximation schemes for multicriteria cycle cover and graph factor problems.
 Publication:

arXiv eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:cs/0606040
 Bibcode:
 2006cs........6040M
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Computational Complexity;
 F.2.2;
 G.2.1;
 G.2.2
 EPrint:
 A preliminary version has been presented at the 4th Workshop on Approximation and Online Algorithms (WAOA 2006). 22 pages