Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
The Constrained Minimum Spanning Tree Problem (Extended Abstract)
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
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
Approximating the Pareto curve with local search for the bicriteria TSP(1,2) problem
Theoretical Computer Science
Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs
Journal of the ACM (JACM)
Multicriteria Optimization
An improved approximation algorithm for the asymmetric TSP with strengthened triangle inequality
Journal of Discrete Algorithms
Approximating Multi-criteria Max-TSP
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Improved Approximation Ratios for Traveling Salesperson Tours and Paths in Directed Graphs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
A 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
An O(log n/ log log n)-approximation algorithm for the asymmetric traveling salesman problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
(Non)-approximability for the multi-criteria TSP(1, 2)
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Deterministic algorithms for multi-criteria Max-TSP
Discrete Applied Mathematics
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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We present approximation algorithms for almost all variants of the multicriteria traveling salesman problem (TSP). First, we devise randomized approximation algorithms for multicriteria maximum traveling salesman problems (Max-TSP). For multicriteria Max-STSP where the edge weights have to be symmetric, we devise an algorithm with an approximation ratio of 2/3 - ϵ. For multicriteria Max-ATSP where the edge weights may be asymmetric, we present an algorithm with a ratio of 1/2 - ϵ. Our algorithms work for any fixed number k of objectives. Furthermore, we present a deterministic algorithm for bicriteria Max-STSP that achieves an approximation ratio of 7/27. Finally, we present a randomized approximation algorithm for the asymmetric multicriteria minimum TSP with triangle inequality (Min-ATSP). This algorithm achieves a ratio of log n + ϵ.