The traveling salesman problem with distances one and two
Mathematics of Operations Research
Performance Guarantees for Approximation Algorithms Depending on Parametrized Triangle Inequalities
SIAM Journal on Discrete Mathematics
Improved approximation algorithms for uniform connectivity problems
Journal of Algorithms
Approximation algorithms for finding highly connected subgraphs
Approximation algorithms for NP-hard problems
Relaxing the Triangle Inequality in Pattern Matching
International Journal of Computer Vision
Nearly linear time approximation schemes for Euclidean TSP and other geometric problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Finding a hamiltonian cycle in the square of a block
Finding a hamiltonian cycle in the square of a block
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Approximations for ATSP with Parametrized Triangle Inequality
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Stability of Approximation Algorithms for Hard Optimization Problems
SOFSEM '99 Proceedings of the 26th Conference on Current Trends in Theory and Practice of Informatics on Theory and Practice of Informatics
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
On the stability of approximation for hamiltonian path problems
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Reoptimizing the strengthened metric TSP on multiple edge weight modifications
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
| Hi-index | 0.00 |
We consider the approximability of the tsp problem in graphs that satisfy a relaxed form of triangle inequality. More precisely, we assume that for some parameter Τ ≥ 1, the distances satisfy the inequality dist(x, y) ≤ Τċ(dist(x, z)+dist(z, y)) for every triple of vertices x, y, and z. We obtain a 4Τ approximation and also show that for some Ɛ 0 it is np-hard to obtain a (1+ ƐΤ) approximation. Our upper bound improves upon the earlier known ratio of (3Τ2=2+Τ2) [1] for all values of Τ