Matching is as easy as matrix inversion
Combinatorica
The complexity of restricted spanning tree problems
Journal of the ACM (JACM)
Approximation algorithms for the TSP with sharpened triangle inequality
Information Processing Letters
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
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)
8/7-approximation algorithm for (1,2)-TSP
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Multicriteria Optimization
An improved approximation algorithm for the asymmetric TSP with strengthened triangle inequality
Journal of Discrete Algorithms
On the relationship between ATSP and the cycle cover problem
Theoretical Computer Science
Derandomizing the Isolation Lemma and Lower Bounds for Circuit Size
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
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
An improved approximation algorithm for the ATSP with parameterized triangle inequality
Journal of Algorithms
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
Multi-Criteria TSP: min and max combined
WAOA'09 Proceedings of the 7th 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
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We present deterministic approximation algorithms for the multi-criteria traveling salesman problem (TSP). Our algorithms are faster and simpler than the existing randomized algorithms. First, we devise algorithms for the symmetric and asymmetric multicriteria Max-TSP that achieve ratios of 1/2k - ε and 1/(4k - 2) - ε, respectively, where k is the number of objective functions. For two objective functions, we obtain ratios of 3/8-ε and 1/4-ε for the symmetric and asymmetric TSP, respectively. Our algorithms are self-contained and do not use existing approximation schemes as black boxes. Second, we adapt the generic cycle cover algorithm for Min-TSP. It achieves ratios of 3/2+ε, 1/2 + γ3/1-3γ2 +ε, and 1/2 + γ2/1-γ + ε for multicriteria Min-ATSP with distances 1 and 2, Min-ATSP with γ-triangle inequality and Min-STSP with γ-triangle inequality, respectively.