Approximation of Pareto optima in multiple-objective, shortest-path problems
Operations Research
The traveling salesman problem with distances one and two
Mathematics of Operations Research
On the complexity of equilibria
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A Hamiltonian Approach to the Assignment of Non-reusable Frequencies
Proceedings of the 18th Conference on Foundations of Software Technology and Theoretical Computer Science
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Deterministic algorithms for multi-criteria TSP
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
On approximating multicriteria TSP
ACM Transactions on Algorithms (TALG)
Multi-Criteria TSP: min and max combined
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Approximation algorithms for multi-criteria traveling salesman problems
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Single approximation for biobjective max TSP
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Approximation with a fixed number of solutions of some biobjective maximization problems
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Single approximation for the biobjective Max TSP
Theoretical Computer Science
Approximation with a fixed number of solutions of some multiobjective maximization problems
Journal of Discrete Algorithms
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Many papers deal with the approximability of multi-criteria optimization problems but only a small number of non-approximability results, which rely on NP-hardness, exist in the literature. In this paper, we provide a new way of proving non-approximability results which relies on the existence of a small size good approximating set (i.e. it holds even in the unlikely event of P=NP). This method may be used for several problems but here we illustrate it for a multi-criteria version of the traveling salesman problem with distances one and two (TSP(1,2)). Following the article of Angel et al. (FCT 2003) who presented an approximation algorithm for the bi-criteria TSP(1,2), we extend and improve the result to any number k of criteria.