Approximation Hardness of TSP with Bounded Metrics
The general asymmetric (and metric) TSP is known to be approximable only to within an O(log n) factor, and is also known to be approximable within a constant factor as soon as the metric is bounded. In this paper we study the asymmetric and symmetric TSP problems with bounded metrics and prove approximation lower bounds of 101/100 and 203/202, respectively, for these problems. We prove also approximation lower bounds of 321/320 and 743/742 for the asymmetric and symmetric TSP with distances one and two.
KeywordsTravel Salesman Problem Travel Salesman Problem Extra Cost Hamiltonian Path Optimum Tour
Unable to display preview. Download preview PDF.
- 2.P. Berman and M. Karpinski. On some tighter inapproximability results. In Proc. 26th ICALP, vol. 1644 of LNCS, pp 200–209, 1999.Google Scholar
- 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. 17th STACS, vol. 1770 of LNCS, pp 382–391, 2000.Google Scholar
- 5.N. Christofides. Worst-case analysis of a new heuristic for the traveling salesman problem. Technical Report CS-93-13, GSIA, Carnegie Mellon University, 1976.Google Scholar
- 8.J. Håstad. Some optimal inapproximability results. In Proc. 29th STOC, pp 1–10, 1997.Google Scholar
- 9.R. M. Karp. Reducibility among combinatorial problems. In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, pp 85–103. Plenum Press, New York, 1972.Google Scholar
- 10.C. H. Papadimitriou and S. Vempala. On the approximability of the traveling salesman problem. In Proc. 32nd STOC, pp 126–133, 2000.Google Scholar
- 11.C. H. Papadimitriou and S. Vempala. On the approximability of the traveling salesman problem. Manuscript, 2001.Google Scholar
- 13.L. Trevisan. When Hamming meets Euclid: The approximability of geometric TSP and MST. In Proc. 29th STOC, pp 21–29, 1997.Google Scholar