Approximation algorithms for the euclidean traveling salesman problem with discrete and continuous neighborhoods

International Journal of Computational Geometry and Applications

Volumn 19, Issue 2, 2009, Pages 173-193

  Elbassioni, Khaled ^a   Fishkin, Aleksei V ^b   Sitters, René ^c  

^a MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

^b SIEMENS AG   (Germany)

^c VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

Approximation algorithms; Connected neighborhoods; Euclidean TSP; Fat objects; Group Steiner tree; Packing lemmas

Indexed keywords

EID: 66449105239     PISSN: 02181959     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218195909002897     Document Type: Conference Paper

References (20)

1. E. M. Arkin and R. Hassin, Approximation algorithms for the geometric covering salesman problem, Discr. Appl. Math. 55( 3) ( 1994) 197-218.
2. S. Arora, Nearly linear time approximation schemes for euclidean TSP and other geometric problems, J. ACM 45( 5) ( 1998) 1-30. (Pubitemid 128497506)
3. H. Chan and K. Elbassioni, A QPTAS for TSP with Fat Weakly Disjoint Neighborhoods in Doubling Metrics, Tech. Report 2009-2101, DIMACS Technical Reports.
4. A. E. F. Clementi, P. Crescenzi and G. Rossi, On the complexity of approximating colored-graph problems, Proc. 5th Internat. Computing and Combinatorics Conference, Lecture Notes in Computer Science, Vol. 1627 (Springer, 1999), pp. 281-290.
5. M. de Berg, J. Gudmundsson, M. J. Katz, C. Levcopoulos, M. H. Overmars and A. F. van der Stappen, TSP with Neighborhoods of varying size, J. Algorithms 57 ( 2005), 22-36.
6. A. Dumitrescu and J. S. B. Mitchell, Approximation algorithms for TSP with neighborhoods in the plane, J. Algorithms 48( 1) ( 2003) 135-159.
7. K. Elbassioni, A. V. Fishkin, N. Mustafa and R. Sitters, Approximation algorithms for Euclidean group TSP, Proc. 15th Internat. Coll. on Automata, Languages and Programming, Lecture Notes in Computer Science, Vol. 3580 (Springer, 2005), pp. 1115-1126.
8. J. Fakcharoenphol, S. Rao and K. Talwar, A tight bound on approximating arbitrary metrics by tree metrics, STOC, 2003, pp. 448-455.
9. N. Garg, G. Konjevod and R. Ravi, A polylogarithmic approximation algorithm for the group Steiner tree problem, J. Algorithms 37( 1) ( 2000) 66-84.
10. J. Gudmundsson and C. Levcopoulos, A fast approximation algorithm for TSP with neighborhoods, Nordic J. Comput. 6( 4) ( 1999) 469-488.
11. E. Halperin and R. Krauthgamer, Polylogarithmic inapproximability, Proc. 35th Ann. ACM Symp. Theory of Computing, 2003, pp. 585-594.
12. C. S. Mata and J. S. B. Mitchell, Approximation algorithms for geometric tour and network design problems (extended abstract), Proc. 11th Ann. ACM Symp. Computational Geometry, 1995, pp. 360-369.
13. J. S. B. Mitchell, Guillotine subdivions approximate polygonal subdivisons: A simple polynomial-time approximation scheme for geometric TSP, k-MST and related problems, SIAM J. Comput. 28( 4) ( 1999) 1298-1309.
14. J. S. B. Mitchell, Handbook of computational geometry, ch. Geometric Shortest Paths and Network Optimization (Elsevier, North-Holland, Amsterdam, 2000), pp. 633-701.
15. J. S. B. Mitchell, A PTAS for TSP with neighborhoods among fat regions in the plane, Proc. 18th Ann. ACM-SIAM Symp. Discrete Algorithms, 2007, pp. 11-18.
16. G. Reich and P. Widmayer, Beyond Steiner's problem: a VLSI oriented generalization, Proc. 15th Int. Workshop on Graph-theoretic Concepts in Computer Science (Springer, 1990), pp. 196-210.
17. S. Safra and O. Schwartz, On the complexity of approximating TSP with Neighborhoods and related problems, Proc. 11th Annual European Symp. Algorithms, Lecture Notes in Computer Science, Vol. 2832 (Springer, 2003), pp. 446-458. (Pubitemid 37325405)
18. P. Slavik, The errand scheduling problem, Tech. report, SUNY, Bualo, USA, 1997.
19. A. F. van der Stappen, Motion planning amidst fat obstacles, Ph.d. dissertation, Utrecht University, Utrecht, the Netherlands, 1994.
20. K. Talwar, Bypassing the Embedding: Algorithms for Low-Dimensional Metrics, 36th, 2004, pp. 281-290.