New Upper Bounds for Maximum Satisfiability

Journal of Algorithms

Volumn 36, Issue 1, 2000, Pages 63-88

  Niedermeier, Rolf ^a   Rossmanith, Peter ^b  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Exact algorithms; Maximum satisfiability; NP complete problems; Parameterized complexity

Indexed keywords

EID: 0346676595     PISSN: 01966774     EISSN: None     Source Type: Journal    
DOI: 10.1006/jagm.2000.1075     Document Type: Article

References (51)

1. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy, Proof verification and hardness of approximation problems, in "Proceedings of the 33d IEEE Symposium on Foundations of Computer Science," pp. 14-23, 1992.
2. T. Asano, K. Hori, T. Ono, and T. Hirata, A theoretical framework of hybrid approaches to MAX SAT, in "Proceedings of the 8th International Symposium on Algorithms and Computation," Lecture Notes in Computer Science, Vol. 1350, pp. 153-162, Springer-Verlag, Berlin/New York, 1997.
3. T. Asano and D. P. Williamson, Improved approximation algorithms for MAX SAT, in "Proceedings of the 11th ACM-SIAM Symposium on Discrete Algorithms," pp. 96-105, 2000.
4. N. Bansal and V. Raman, Upper bounds for MaxSat: Further improved, in "Proceedings of the 10th International Symposium on Algorithms and Computation," Lecture Notes in Computer Science, Vol. 1741, pp. 247-258, Springer-Verlag, Berlin/New York, 1999.
5. R. Battiti and M. Protasi, Reactive Search, a history-base heuristic for MAX-SAT, ACM J. Exper. Algorithmics 2, No. 2 (1997).
6. R. Battiti and M. Protasi, Approximate algorithms and heuristics for MAX-SAT, in "Handbook of Combinatorial Optimization," (D.-Z. Du and P. M. Pardalos, Eds.), (Vol. 1, pp. 77-148, Kluwer Academic, Dordrecht, 1998.
7. n): A no MIS algorithm, in "Proceedings of the 36th IEEE Symposium on Foundations of Computer Science," pp. 444-452, 1995.
8. B. Borchers and J. Furman, A two-phase exact algorithm for MAX-SAT and weighted MAX-SAT problems, J. Combin. Optim. 2 (1999), 465-474.
9. L. Cai and J. Chen, On fixed-parameter tractability and approximability of NP optimization problems, J. Comput. System Sci. 54 (1997), 465-474.
10. J. Chen, I. Kanj, and W. Jia, Vertex cover: Further observations and further improvements, in "Proceedings of the 25th International Workshop on Graph Theoretic Concepts in Computer Science, Ascona, Switzerland, June 1999," Lecture Notes in Computer Science, Vol. 1665, pp. 313-324, Springer-Verlag, Berlin/New York.
11. P. Crescenzi and V. Kann, "A Compendium of NP Optimization Problems," available at http://www.nada.kth.se/theory/problemlist.html, August 1998.
12. P. Crescenzi and V. Kann, How to find the best approximation results - a follow-up to Garey and Johnson, ACM SIGACT News 29, No. 4 (1998), 90-97.
13. E. Dantsin, M. Gavrilovich, E. A. Hirsch, and B. Konev, "Approximation Algorithms for Max SAT: A Better Performance Ratio at the Cost of a Longer Running Time," Technical Report PDMI preprint 14/1998, Steklov Institute of Mathematics at St. Petersburg, 1998; available at http://logic.pdmi.ras.ru/∼hirsch/.
14. M. Davis and H. Putnam, A computing procedure for quantification theory, J. Assoc. Comput. Mach. 7 (1960), 201-215.
15. R. G. Downey and M. R. Fellows, "Parameterized Complexity," Springer-Verlag, Berlin/New York, 1999.
16. R. G. Downey, M. R. Fellows, and U. Stege, Parameterized complexity: A framework for systematically confronting computational intractability, in "Contemporary Trends in Discrete Mathematics: From DIMACS and DIMATIA to the Future," AMS-DIMAC's, Vol. 49, pp. 49-99, Amer. Math. Soc., Providence, RI, 1999.
17. U. Feige and M. X. Goemans, Approximating the value of two prover proof systems, with applications to MAX 2SAT and MAX DICUT, in "3d IEEE Israel Symposium on the Theory of Computing and Systems," pp. 182-189, 1995.
18. M. Garey and D. Johnson, "Computers and Intractability: A Guide to the Theory of NP-completeness," Freeman, San Francisco, 1979.
19. J. Gramm, "Exact Algorithms for Max2Sat: and Their Applications," Diploma thesis, WSI für Informatik, Universität Tübingen, 1999; available at http://www-fs.informatik. uni-tuebingen.de/∼niedermr/publications/index.html.
20. J. Gramm and R. Niedermeier, Faster exact solutions for Max2Sat, in "Proceedings of the 4th Italian Conference on Algorithms and Complexity," Lecture Notes in Computer Science, Vol. 1767, pp. 174-186, Springer-Verlag, Berlin/New York, 2000.
21. P. Hansen and B. Jaumard, Algorithms for the maximum satisfiability problem, Computing 44 (1990), 279-303.
22. J. Håstad, Some optimal inapproximability results, in "Proceedings of the 29th ACM Symposium on Theory of Computing," pp. 1-10, 1997.
23. E. A. Hirsch, Two new upper bounds for SAT, in "Proceedings of the 9th ACM-SIAM Symposium on Discrete Algorithms," pp. 521-530, 1998.
24. E. A. Hirsch, "A New Algorithm for MAX-2-SAT," in "Proceedings of the 17th International Symposium on Theoretical Aspects of Computer Science," Lecture Notes in Computer Science, Vol. 1770, pp. 65-73, Springer-Verlag, Berlin/New York, 2000. [The conference paper contains an error, which is fixed in a revised version of the Technical Report TR99-036, ECCC, Trier.]
25. D. S. Hochbaum, Ed., "Approximation Algorithms for NP-hard Problems," PWS, Boston, 1997.
26. D. S. Johnson and M. A. Trick, Eds., "Cliques, Coloring and Satisfiability, Second DIMACS Implementation Challenge," DIMACS Ser. Discr. Math. Theor. Comput Sci., Vol. 26, Amer. Math. Soc., Providence, RI, 1996.
27. H. Karloff and U. Zwick, A 7/8-approximation algorithm for MAX 3SAT?, in "Proceedings of the 38th IEEE Symposium on Foundations of Computer Science," pp. 406-415, 1997.
28. O. Kullmann, New methods for 3-SAT decision and worst-case analysis, Theoret. Comput. Sci. 223 (1999), 1-72.
29. O. Kullmann and H. Luckhardt, Deciding prepositional tautologies: Algorithms and their complexity, submitted for publication, 1997, available at http://mi.informatik.unifrankfurt.de/people/kullmann/papers.html.
30. M. Mahajan and V. Raman, Parameterizing above guaranteed values: MaxSat and MaxCut, J. Algorithms 31 (1999), 335-354.
31. n steps, Discrete Appl. Math. 10 (1985), 287-295.
32. R. Niedermeier, Some prospects for efficient fixed parameter algorithms (invited paper), in "Proceedings of the 25th Conference on Current Trends in Theory and Practice of Informatics (SOFSEM)" (B. Rovan, Ed.), Lecture Notes in Computer Science, Vol. 1521, pp. 168-185, Springer-Verlag, Berlin/New York, 1998.
33. R. Niedermeier and P. Rossmanith, "A General Method to Speed up Fixed-Parameter-Tractable Algorithms," Technical Report TUM-19913, Institut für Informatik, Technische Universität München, Fed. Rep. of Germany, June 1999. [Revised version to appear in Information Processing Letters.]
34. R. Niedermeier and P. Rossmanith, Upper bounds for vertex cover further improved, in "Proceedings of the 16th Symposium on Theoretical Aspects of Computer Science," (C. Meinel and S. Tison, Eds.), Lecture Notes in Computer Science, Vol. 1563, pp. 561-570, Springer-Verlag, Berlin/New York, 1999.
35. C. H. Papadimitriou, "Computational Complexity," Addison-Wesley, Reading, MA, 1994.
36. C. H. Papadimitriou and M. Yannakakis, Optimization, approximation, and complexity classes, J. Comput. System Sci. 43 (1991), 425-440.
37. R. Paturi, P. Pudlák, M. Saks, and F. Zane, An improved exponential-time algorithm for k-SAT, in "Proceedings of the 39th IEEE Symposium on Foundations of Computer Science," pp. 628-637, 1998.
38. R. Paturi, P. Pudlák, and F. Zane, Satisfiability coding lemma, in "Proceedings of the 38th IEEE Symposium on Foundations of Computer Science," pp. 566-574, 1997.
39. V. Raman, Parameterized complexity, in "Proceedings of the 7th National Seminar on Theoretical Computer Science (Chennai, India)," pp. I-1-I-18, June 1997.
40. J. M. Robson, Algorithms for maximum independent sets, J. Algorithms 7 (1986), 425-440.
41. n) 3-Satisfiability algorithm, Technical Report 96-230, Universität Köln, 1996.
42. n/4) algorithm for certain NP-complete problems, SIAM J. Comput. 10 (1981), 456-464.
43. R. E. Tarjan and A. E. Trojanowski, Finding a maximum independent set, SLAM J. Comput. 6 (1977), 537-550.
44. L. Trevisan, G. Sorkin, M. Sudan, and D. P. Williamson, Gadgets, approximation, and linear programming, in "Proceedings of the 37th IEEE Symposium on Foundations of Computer Science," pp. 617-626, 1996.
45. R. J. Wallace, Enhancing maximum satisfiability algorithms with pure literal strategies, in "11th Canadian Conference on Artificial Intelligence, AI'96," Lecture Notes in Artificial Intelligence, Vol. 1081, pp. 388-401, Springer-Verlag, Berlin/New York, 1996.
46. R. J. Wallace and E. C. Feuder, Comparative studies of constraints satisfaction and Davis-Putnam algorithms for maximum satisfiability problems, in "Cliques, Coloring and Satisfiability, Second DIMACS Implementation Challenge," (D. S. Johnson and M. A. Trick, Eds.), DIMACS Ser. Disc. Math. Theor. Comput. Sci., Vol. 26, Amer. Math. Soc., Providence, RI, 1996.
47. J. Wiedermann, Fast simulation of nondeterministic Turing machines with application to the Knapsack problem, Comput. Artificial Intell. 8 (1989), 591-596.
48. M. Yagiura and T. Ibaraki, Efficient 2 and 3-flip neighborhood search algorithms for the MAX SAT, in "Proceedings of the 4th Annual International Computing and Combinatorics Conference (COCOON)," Lecture Notes in Computer Science, Vol. 1449, pp. 105-116, Springer-Verlag, Berlin, 1998.
49. M. Yannakakis, On the approximation of maximum satisfiability, J. Algorithms 17 (1994), 475-502.
50. W. Zhang, Number of models and satisfiability of sets of clauses, Theoret. Comput. Sci. 155 (1996), 277-288.
51. U. Zwick, Outward rotations: a tool for rounding solutions of semidefinite programming relaxations, with applications to MAX CUT and other problems, in "Proceedings of the 31st ACM Symposium on Theory of Computing," pp. 679-687, 1999.