On the complexity of approximating tsp with neighborhoods and related problems

Computational Complexity

Volumn 14, Issue 4, 2006, Pages 281-307

  Safra, Shmuel ^a   Schwartz, Oded ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Approximation; Hardness of approximation; Inapproximability; NP optimization problems; TSP; TSP with neighborhoods

Indexed keywords

EID: 33644891322     PISSN: 10163328     EISSN: 14208954     Source Type: Journal    
DOI: 10.1007/s00037-005-0200-3     Document Type: Article

References (31)

1. E. ARKIN & R. HASSIN (1994). Approximation algorithms for the geometric covering salesman problem. Discrete Appl. Math. 55, 197-218.
2. S. ARORA (1998). Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems. J. ACM 45, 753-782.
3. M. DE BERG, J. GUDMUNDSSON, M. J. KATZ, C. LEVCOPOULOS, M. H. OVER-MARS & A. F. VAN DER STAPFEN (2002). TSP with neighborhoods of varying size. In Annual European Symposium on Algorithms, 187-199.
4. S. CARLSSON, H. JONSSON & B. J. NILSSON (1999). Finding the shortest watchman route in a simple polygon. Discrete Comput. Geom. 22, 377-402.
5. W. CHIN & S. NTAFOS (1988). Optimum watchman routes. Inform. Process. Lett. 28, 39-44.
6. N. CHRISTOFIDES (1976). Worst-case analysis of a new heuristic for the traveling salesman problem. Technical report, Graduate School of Industrial Administration, Carnegy-Mellon Univ.
7. I. DINUR, V. GURUSWAMI, S. KHOT & O. REGEV (2003). A new multilayered PCP and the hardness of hypergraph vertex cover. In Proc. 35th ACM Symposium on Theory of Computing, ACM Press, 595-601.
8. A. DUMITRESCU & J. S. B. MITCHELL (2003). Approximation algorithms for TSP with neighborhoods in the plane. J. Algorithms 48, 135-159.
9. L. ENGEBRETSEN & M. KARPINSKI (2001). Approximation hardness of TSP with bounded metrics. In Annual International Colloquium on Automata, Languages and Programming, 201-212.
10. U. FEIGE (1998). A threshold of Inn for approximating set cover. J. ACM 45, 634-652.
11. A. FRIEZE, G. GALBIATI & F. MAFFIOLI (1982). On the worst-case performance of some algorithms for the asymmetric travelling salesman problem. Networks 12, 23-39.
12. M. R. GAREY, R. L. GRAHAM & D. S. JOHNSON (1976). Some NP-complete geometric problems. In Conf. Record 8th Annual ACM Symposium on Theory of Computing (Hershey, PA), 10-22.
13. M. R. GAREY, R. L. GRAHAM & D. S. JOHNSON (1977). The complexity of computing Steiner minimal trees. SIAM J. Appl. Math. 32, 835-859.
14. L. GEWALI & S. C. NTAFOS (1998). Watchman routes in the presence of a pair of convex polygons. Inform. Sci. 105, 123-149.
15. J. GUDMUNDSSON & C. LEVCOPOULOS (1999). A fast approximation algorithm for TSP with neighborhoods. Nordic J. Comput. 6, 469-488.
16. E. HALPERIN & R. KRAUTHGAMER (2003). Polylogarithmic inapproximability. In Proc. 35th ACM Symposium on Theory of Computing, ACM Press, 585-594.
17. J. HOLMERIN (2002). Vertex cover on 4-regular hyper-graphs is hard to approximate within 2 - ε. In ACM Symposium on Theory of Computing (STOC), 544-552.
18. E. IHLER (1992). The complexity of approximating the class Steiner tree problem. In Graph-Theoretic Concepts in Computer Science, G. Schmidt and R. Berghammer (eds.), Lecture Notes in Comput SCi. 570, Springer, 85-96.
19. G. KINDLER (2004). Personal communication.
20. C. LUND& M. YANNAKAKIS (1994). On the hardness of approximating minimization problems. J. ACM 41, 960-981.
21. C. MATA & J. S. B. MITCHELL (1995). Approximation algorithms for geometric tour and network design problems. In Proc. 11th Annual Symposium on Computational Geometry, ACM Press, 360-369.
22. J. S. B. MITCHELL (1999). Guillotine subdivisions approximate polygonal subdivisions: a simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems. SIAM J. Comput. 28, 1298-1309.
23. J. S. B. MITCHELL (2000). Geometric Shortest Paths and Network Optimization. Elsevier Science, preliminary edition.
24. B. J. NILSSON & D. WOOD (1990). Optimum watchmen in spiral polygons. In CCCG: Canadian Conference in Computational Geometry, 269-272.
25. C. H. PAPADIMITRIOU (1977). Euclidean TSP is NP-complete. Theoret. Comput. Sci. 4, 237-244.
26. C. H. PAPADIMITRIOU & S. VEMPALA (2000). On the approximability of the traveling salesman problem (extended abstract). In Proc. 32nd Annual ACM Symposium on Theory of Computing, ACM Press, 126-133.
27. E. PETRANK (1994). The hardness of approximation: gap location. Comput. Complexity 4, 133-157.
28. R. RAZ & S. SAFRA (1997). A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP. In Proc. 29th Annual ACM Symposium on Theory of Computing, ACM Press, 475-484.
29. O. SCHWARTZ (2002). On the hardness of approximating TSP with neighborhoods, group TSP and group Steiner tree. Master's thesis, Tel-Aviv Univ.
30. P. SLAVIK (1997). The errand scheduling problem. Technical Report 97-02, SUNY at Buffalo.
31. T. XUE-HOU, T. HIRATA & Y. INAGAKI (1993). An incremental algorithm for constructing shortest watchman routes. Internat. J. Comput. Geom. Appl. 3, 351-365.