Improved lower bounds on the approximability of the traveling salesman problem

Theoretical Informatics and Applications

Volumn 34, Issue 3, 2000, Pages 213-255

  Böckenhauer, Hans Joachim ^a   Seibert, Sebastian ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; FORMAL LANGUAGES; LINEAR EQUATIONS; POLYNOMIALS; PROBLEM SOLVING; THEOREM PROVING;

ENGEBRETSEN METHOD; EUCLIDEAN TRAVELING SALESMAN PROBLEMS; POLYNOMIAL TIME APPROXIMATION ALGORITHM; THRESHOLD LANGUAGES;

TRAVELING SALESMAN PROBLEM;

EID: 0342521535     PISSN: 09883754     EISSN: None     Source Type: Journal    
DOI: 10.1051/ita:2000115     Document Type: Article

References (19)

1. T. Andreae and H.-J. Bandelt, Performance guarantees for approximation algorithms depending on parametrized triangle inequalities. SIAM J. Discrete Math. 8 (1995) 1-16.
2. S. Arora, Polynomial Time Approximation Schemes for Euclidean Traveling Salesman and Other Geometric Problems. J. ACM 45 (1998) 753-782.
3. S. Arora, Nearly linear time approximation schemes for Euclidean TSP and other geometric problems, in Proc. 38th Ann. Symp. on Foundations of Comp. Sci. (FOCS '97), IEEE (1997) 554-563.
4. S. Arora and C. Lund, Hardness of Approximations, Chapter 10 of [12], pp. 399-446.
5. M.A. Bender and C. Chekuri, Performance guarantees for the TSP with a parameterized triangle inequality. Inform. Process. Lett. 73 (2000) 17-21.
6. H.-J. Böckenhauer, J. Hromkovič, R. Klasing, S. Seibert and W. Unger, Towards the Notion of Stability of Approximation Algorithms and the Traveling Salesman Problem (Extended Abstract), edited by G.C. Bongiovanni, G. Gambosi and R. Petreschi, Algorithms and Complexity, Proc. 4th Italian Conference CIAC 2000. Springer, Lecture Notes in Comput. Sci. 1767 (2000) 72-86. (Full version in: Electronic Colloquium on Computational Complexity (http://www.eccc.uni-trier.de/eccc/), Report No. 31 (1999).)
7. H.-J. Böckenhauer, J. Hromkovič, R. Klasing, S. Seibert and W. Unger, Towards the Notion of Stability of Approximation Algorithms and the Traveling Salesman Problem (Extended Abstract), edited by G.C. Bongiovanni, G. Gambosi and R. Petreschi, Algorithms and Complexity, Proc. 4th Italian Conference CIAC 2000. Springer, Lecture Notes in Comput. Sci. 1767 (2000) 72-86. (Full version in: Electronic Colloquium on Computational Complexity (http://www.eccc.uni-trier.de/eccc/), Report No. 31 (1999).)
8. H.-J. Böckenhauer, J. Hromkovič, R. Klasing, S. Seibert and W. Unger, An Improved Lower Bound on the Approximability of Metric TSP and Approximation Algorithms for the TSP with Sharpened Triangle Inequality (Extended Abstract), edited by H. Reichel and S. Tison, STACS 2000, Proc. 17th Ann. Symp. on Theoretical Aspects of Comp. Sci., Springer, Lecture Notes in Comput. Sci. 1770 (2000) 382-394.
9. H.-J. Böckenhauer, J. Hromkovič, R. Klasing, S. Seibert and W. Unger, Approximation Algorithms for the TSP with Sharpened Triangle Inequality. Inform. Process. Lett. 75 (2000) 133-138.
10. P. Berman and M. Karpinski, On some tighter inapproximability results. Technical Report TR98-029, Electronic Colloquium on Computational Complexity (1998) http://www.eccc.uni-trier.de/eccc/
11. N. Christofides, Worst-case analysis of a new heuristic for the traveling salesman problem, Technical Report 388. Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh (1976).
12. L. Engebretsen, An explicit lower bound for TSP with distances one and two. Extended abstract, edited by C. Meinel and S. Tison, STACS 99, Proc. 16th Ann. Symp. on Theoretical Aspects of Comp. Sci. Springer, Lecture Notes in Comput. Sci. 1563 (1999) 373-382. Full version in: Electronic Colloquium on Computational Complexity (http://www.eccc.unitrier.de/eccc/), Revision 1 of Report No. 46 (1999).
13. L. Engebretsen, An explicit lower bound for TSP with distances one and two. Extended abstract, edited by C. Meinel and S. Tison, STACS 99, Proc. 16th Ann. Symp. on Theoretical Aspects of Comp. Sci. Springer, Lecture Notes in Comput. Sci. 1563 (1999) 373-382. Full version in: Electronic Colloquium on Computational Complexity (http://www.eccc.unitrier.de/eccc/), Revision 1 of Report No. 46 (1999).
14. D.S. Hochbaum, Approximation Algorithms for NP-hard Problems. PWS Publishing Company (1996).
15. E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys, The Traveling Salesman Problem. John Wiley & Sons (1985).
16. I.S.B. Mitchell, Guillotine subdivisions approximate polygonal subdivisions: Part II - a simple polynomial-time approximation scheme for geometric k-MST, TSP and related problems. Technical Report, Dept. of Applied Mathematics and Statistics, Stony Brook (1996).
17. E.W. Mayr, H.J. Prömel and A. Steger, Lectures on Proof Verification and Approximation Algorithms. Springer, Lecture Notes in Comput. Sci. 1967 (1998).
18. Ch. Papadimitriou and S. Vempala, On the approximability of the traveling salesman problem, in Proc. 32nd Ann. Symp. on Theory of Comp. (STOC '00), ACM (2000).
19. Ch. Papadimitriou and M. Yannakakis, The traveling salesman problem with distances one and two. Math. Oper. Res. 18 (1993) 1-11.