Complexity of the exact domatic number problem and of the exact conveyor flow shop problem

Theory of Computing Systems

Volumn 39, Issue 5, 2006, Pages 635-668

  Riege, Tobias ^a   Rothe, Jörg ^a  

^a HEINRICH HEINE UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONVEYOR FLOW SHOP; DISJOINT DOMINATING SETS; DOMATIC NUMBER; DOMATIC NUMBER PROBLEM; DOMINATING SET PROBLEMS;

COMPUTER SCIENCE; MATHEMATICAL TECHNIQUES;

CONVEYORS;

EID: 33748523066     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s00224-004-1209-8     Document Type: Article

References (59)

1. [Ad] L. Adleman. Two theorems on random polynomial time. In Proceedings of the 19th IEEE Symposium on Foundations of Computer Science, pages 75-83, 1978.
2. [AH] E. Allender and L. Hemachandra. Lower bounds for the low hierarchy. Journal of the ACM, 39(1):234-251, 1992.
3. +] A. Bertoni, D. Bruschi, D. Joseph, M. Sitharam, and P. Young. Generalized boolean hierarchies and boolean hierarchies over RP. In Proceedings of the 7th Conference on Fundamentals of Computation Theory, pages 35-46. Lecture Notes in Computer Science #380. Springer-Verlag, Berlin, August 1989.
4. [BCO] R. Beigel, R. Chang, and M. Ogiwara. A relationship between difference hierarchies and relativized polynomial hierarchies. Mathematical Systems Theory, 26(3):293-310, 1993.
5. [Be1] R. Beigel. Bounded queries to SAT and the boolean hierarchy. Theoretical Computer Science, 84(2):199-223, 1991.
6. [Be2] R. Beigel. Perceptrons, PP, and the polynomial hierarchy. Computational Complexity, 4(4):339-349, 1994.
7. [BH] S. Buss and L. Hay. On truth-table reducibility to SAT. Information and Computation, 91(1):86-102, March 1991.
8. [BHW] R. Beigel, L. Hemachandra, and G. Wechsung. Probabilistic polynomial time is closed under parity reductions. Information Processing Letters, 37(2):91-94, 1991.
9. [BKT] H. Buhrman, J. Kadin, and T. Thierauf. On functions computable with nonadaptive queries to NP. In Proceedings of the 9th Structure in Complexity Theory Conference, pages 43-52. IEEE Computer Society Press, Los Alamitos, CA, 1994.
10. [BLS] A. Brandstädt, V. Le, and J. Spinrad. Graph Classes: A Survey. SIAM Monographs on Discrete Mathematics and Applications. Society for Industrial and Applied Mathematics, Philadelphia, PA, 1999.
11. [Bo] M. Bonuccelli. Dominating sets and dominating number of circular arc graphs. Discrete Applied Mathematics, 12:203-213, 1985.
12. +1] J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy I: Structural properties. SIAM Journal on Computing, 17(6):1232-1252, 1988.
13. +2] J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95-111, 1989.
14. [CK] R. Chang and J. Kadin. The boolean hierarchy and the polynomial hierarchy: a closer connection. SIAM Journal on Computing, 25(2):340-354, April 1996.
15. p-complete. SIAM Journal on Computing, 16(2):259-277, April 1987.
16. [Es] W. Espelage. Bewegungsminimierung in der Förderband-Flow-Shop- Verarbeitung. Ph.D. thesis, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, 2001. In German.
17. [EW1] W. Espelage and E. Wanke. Movement optimization in flow shop processing with buffers. Mathematical Methods of Operations Research, 51(3):495-513, 2000.
18. [EW2] W. Espelage and E. Wanke. A 3-approximation algorithmus for movement minimization in conveyor flow shop processing. In Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science, pages 363-374. Lecture Notes in Computer Science #2136. Springer-Verlag, Berlin, 2001.
19. [EW3] W. Espelage and E. Wanke. Movement minimization for unit distances in conveyor flow shop processing. Mathematical Methods of Operations Research, 57(2):172-206, 2003.
20. [Fa] M. Farber. Domination, independent domination, and duality in strongly chordal graphs. Discrete Applied Mathematics, 7:115-130, 1984.
21. [FHK] U. Feige, M. Halldórsson, and G. Kortsarz. Approximating the domatic number. In Proceedings of the 32nd ACM Symposium on Theory of Computing, pages 134-143. ACM Press, New York, May 2000.
22. [Gi] J. Gill. Computational complexity of probabilistic Turing machines. SIAM Journal on Computing, 6(4):675-695, 1977.
23. [GJ] M. Garey and D. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York, 1979.
24. [GK] V. Guruswami and S. Khanna. On the hardness of 4-coloring a 3-colorable graph. In Proceedings of the 15th Annual IEEE Conference on Computational Complexity, pages 188-197. IEEE Computer Society Press, Los Alamitos, CA, May 2000.
25. [GNW] T. Gundermann, N. Nasser, and G. Wechsung. A survey on counting classes. In Proceedings of the 5th Structure in Complexity Theory Conference, pages 140-153. IEEE Computer Society Press, Los Alamitos, CA, July 1990.
26. [Go] M. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, 1980.
27. [GRW1] A. Große, J. Rothe, and G. Wechsung. Relating partial and complete solutions and the complexity of computing smallest solutions. In Proceedings of the Seventh Italian Conference on Theoretical Computer Science, pages 339-356. Lecture Notes in Computer Science #2202. Springer-Verlag, Berlin, October 2001.
28. [GRW2] A. Große, J. Rothe, and G. Wechsung. Computing complete graph isomorphisms and hamiltonian cycles from partial ones. Theory of Computing Systems, 35(1):81-93, February 2002.
29. [Ha] F. Hausdorff. Grundzüge der Mengenlehre de Gruyter, Leipzig, 1914.
30. [He] L. Hemachandra. The strong exponential hierarchy collapses. Journal of Computer and System Sciences, 39(3):299-322, 1989.
31. [HHR1] E. Hemaspaandra, L. Hemaspaandra, and J. Rothe. Exact analysis of Dodgson elections: Lewis Carroll's 1876 voting system is complete for parallel access to NP. Journal of the ACM, 44(6):806-825, November 1997.
32. [HHR2] E. Hemaspaandra, L. Hemaspaandra, and J. Rothe. Raising NP lower bounds to parallel NP lower bounds. SIGACT News, 28(2):2-13, June 1997.
33. [HHW] L. Hemaspaandra, H. Hempel, and G. Wechsung. Query order. SIAM Journal on Computing, 28(2):637-651, 1999.
34. [HR1] L. Hemaspaandra and J. Rothe. Unambiguous computation: Boolean hierarchies and sparse Turing-complete sets. SIAM Journal on Computing, 26(3):634-653, June 1997.
35. [HR2] E. Hemaspaandra and J. Rothe. Recognizing when greed can approximate maximum independent sets is complete for parallel access to NP. Information Processing Letters, 65(3):151-156, February 1998.
36. [HRS] E. Hemaspaandra, J. Rothe, and H. Spakowski. Recognizing when heuristics can approximate minimum vertex covers is complete for parallel access to NP. In Proceedings of the 28th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2002), pages 258-269. Lecture Notes in Computer Science #2573. Springer-Verlag, Berlin, June 2002.
37. [HT] P. Heggernes and J. Telle. Partitioning graphs into generalized dominating sets. Nordic Journal of Computing, 5(2):128-142, 1998.
38. [HW] L. Hemachandra and G. Wechsung. Kolmogorov characterizations of complexity classes. Theoretical Computer Science, 83:313-322, 1991.
39. [JT] B. Jenner and J. Torán. Computing functions with parallel queries to NP. Theoretical Computer Science, 141:175-193, 1995.
40. [Ka1] J. Kadin. The polynomial time hierarchy collapses if the boolean hierarchy collapses. SIAM Journal on Computing, 17(6):1263-1282, 1988. Erratum, ibid., 20(2):404, 1991.
41. NP[log n] and sparse Turing-complete sets for NP. Journal of Computer and System Sciences, 39(3):282-298, 1989.
42. [Ko1] K. Ko. Relativized polynomial time hierarchies having exactly k levels. SIAM Journal on Computing, 18(2):392-408, 1989.
43. [Ko2] K. Ko. On adaptive versus nonadaptive bounded query machines. Theoretical Computer Science, 82:51-69, 1991.
44. [Kr] M. Krentel. The complexity of optimization problems. Journal of Computer and System Sciences, 36:490-509, 1988.
45. [KS] H. Kaplan and R. Shamir. The domatic number problem on some perfect graph families. Information Processing Letters, 49(1):51-56, January 1994.
46. [KSW] J. Köbler, U. Schöning, and K. Wagner. The difference and truth-table hierarchies for NP. R.A.I.R.O. Informatique théorique et Applications, 21:419-435, 1987.
47. [LS] T. Long and M. Sheu. A refinement of the low and high hierarchies. Mathematical Systems Theory, 28(4):299-327, July/August 1995.
48. [Og1] M. Ogiwara. Generalized theorems on relationships among reducibility notions to certain complexity classes. Mathematical Systems Theory, 27(3):189-200, 1994.
49. [Og2] M. Ogihara. Functions computable with limited access to NP. Information Processing Letters, 58(1):35-38, May 1996.
50. [Pa] C. Papadimitriou. Computational Complexity. Addison-Wesley, Reading, MA, 1994.
51. [PY] C. Papadimitriou and M. Yannakakis. The complexity of facets (and some facets of complexity). Journal of Computer and System Sciences, 28(2):244-259, 1984.
52. [PZ] C. Papadimitriou and S. Zachos. Two remarks on the power of counting. In Proceedings of the 6th GI Conference on Theoretical Computer Science, pages 269-276. Lecture Notes in Computer Science #145. Springer-Verlag, Berlin, 1983.
53. [Ri] T. Riege. Vollständige Probleme in der Booleschen Hierarchie über NP. Diploma thesis, Heinrich-Heine-Universität Düsseldorf, Institut für Informatik, Düsseldorf, August 2002. In German.
54. [Ro] J. Rothe. Exact complexity of Exact-Four-Colorability. Information Processing Letters, 87(1):7-12, July 2003.
55. [RSV] J. Rothe, H. Spakowski, and J. Vogel. Exact complexity of the winner problem for Young elections. Theory of Computing Systems, 36(4):375-386, June 2003.
56. [Sc] T. Schaefer. The complexity of satisfiability problems. In Proceedings of the 10th ACM Symposium on Theory of Computing, pages 216-226. ACM Press, New York, May 1978.
57. [Va] L. Valiant. The relative complexity of checking and evaluating. Information Processing Letters, 5(1):20-23, 1976.
58. [Wa1] K. Wagner. More complicated questions about maxima and minima, and some closures of NP. Theoretical Computer Science, 51:53-80, 1987.
59. [Wa2] K. Wagner. Bounded query classes. SIAM Journal on Computing, 19(5):833-846, 1990.