Approximation algorithms for the traveling salesman problem with range condition

 Access to full text

 Full (PDF)

1. [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. Zbl0832.90089MR1315955
2. [2] M. A. Bender and C. Chekuri, Performance guarantees for the TSP with a parametrized triangle inequality, in Proc. WADS'99. Springer, Lecture Notes in Comput. Sci. 1663 (1999) 80-85. Zbl1063.68700MR1734094
3. [3] 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, in Proc. STACS 2000. Springer, Lecture Notes in Comput. Sci. (to appear). Zbl1028.90044MR1776665
4. [4] 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, in Electronic Colloquium on Computational Complexity. Report No. 31 (1999). Zbl1094.90036
5. [5] 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). 
6. [6] J. Edmonds and E. L. Johnson, Matching: A well-solved class of integer linear programs, in Proc. Calgary International conference on Combinatorial Structures and Their Applications. Gordon and Breach (1970) 88-92. Zbl0258.90032MR267898
7. [7] M. R. Garey, R. L. Graham and D. J. Johnson, Some NP-cornplete geometric problems, in Proc. ACM Symposium on Theory of Computing (1976) 10-22. Zbl0377.68036
8. [8] H. N. Gabow and R. E. Tarjan, Faster scaling algorithms for general graph-matching problems. J. ACM 28 (1991) 815-853. Zbl0799.68145MR1134518
9. [9] J. Hromkovič, Stability of approximation algorithms for hard optimisation problems, in Proc. SOFSEM'99. Springer-Verlag, Lecture Notes in Comput. Sci. 1725 (1999) 29-46. Zbl0961.65060MR1784516
10. [10] J. Hromkovič, Stability of approximation algorithms and the knapsack problem, in Jewels are forever, edited by J. Karhumäki, H. Maurer and G. Rozenberg. Springer-Verlag (1999) 238-249. Zbl0945.68074MR1719081
11. [11] C. H. Papadimitriou, Euclidean TSP is NP-complete. TCS 4 (1977) 237-244. Zbl0386.90057MR455550
12. [12] C. H. Papadimitriou and M. Yannakakis, The Traveling salesman problem with distances one and two. Math. Oper. Res. 18 (1993) 1-11. Zbl0778.90057MR1250103