Incomplete algorithms

Frontiers in Artificial Intelligence and Applications

Volumn 185, Issue 1, 2009, Pages 185-203

  Kautz, Henry ^a   Sabharwal, Ashish ^a   Selman, Bart ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

STOCHASTIC SYSTEMS;

BACKTRACKING SEARCH; GREEDY ALGORITHMS; LOCAL MINIMUMS; PERFORMANCE; RANDOM INSTANCE; RANDOMISATION; RE-WEIGHTING; SAT SOLVERS; SATISFIABILITY TESTING; STOCHASTIC LOCAL SEARCHES;

LAGRANGE MULTIPLIERS;

EID: 72949085767     PISSN: 09226389     EISSN: 18798314     Source Type: Book Series    
DOI: 10.3233/978-1-58603-929-5-185     Document Type: Article

References (104)

1. D. Achlioptas. Setting 2 variables at a time yields a new lower bound for random 3-SAT. In 32nd STOC, pages 28-37, Portland,OR, May 2000.
2. E. Aurell, U. Gordon, and S. Kirkpatrick. Comparing beliefs, surveys, and random walks. In 18th NIPS, Vancouver, BC, December 2004.
3. H. M. Adorf and M. D. Johnston. A discrete stochastic neural network algorithm for constraint satisfaction problems. In Intl. Joint Conf. on Neural Networks, pages 917-924, San Diego, CA, 1990.
4. D. Achlioptas, A. Naor, and Y. Peres. Rigorous location of phase transitions in hard optimization problems. Nature, 435:759-764, 2005.
5. D. Achlioptas and Y. Peres. The threshold for random k-SAT is 2k(ln 2 - O(k)). J. American Math. Soc., 17:947-973, 2004.
6. Anbulagan, D. N. Pham, J. K. Slaney, and A. Sattar. Old resolution meets modern SLS. In 20th AAAI, pages 354-359, Pittsburgh, PA, July 2005.
7. D. Achlioptas and F. Ricci-Tersenghi. On the solution-space geometry of random constraint satisfaction problems. In 38th STOC, pages 130-139, Seattle, WA, May 2006.
8. D. Achlioptas and G. Sorkin. Optimal myopic algorithms for random 3-SAT. In 41st FOCS, pages 590-600, Redondo Beach, CA, November 2000. IEEE.
9. B. Bollob́as, C. Borgs, J. T. Chayes, J. H. Kim, and D. B. Wilson. The scaling window of the 2-SAT transition. Random Struct. and Alg., 19(3-4):201-256, 2001.
10. A. Broder, A. Frieze, and E. Upfal. On the satisfiability and maximum satisfiability of random 3-CNF formulas. In Proc., 4th SODA, January 1993.
11. P. Beame, R. Karp, T. Pitassi, and M. Saks. On the Complexity of Unsatisfiability Proofs for Random k-CNF Formulas. In 30th STOC, pages 561-571, Dallas, TX, May 1998.
12. P. W. Beame and T. Pitassi. Simplified and improved resolution lower bounds. In 37th FOCS, pages 274-282, Burlington, VT, October 1996. IEEE.
13. A. Braunstein and R. Zecchina. Survey propagation as local equilibrium equations. J. Stat. Mech., P06007, 2004.
14. J. M. Crawford and L. D. Auton. Experimental results on the crossover point in satisfiability problems. In Proc. AAAI-93, pages 21-27, Washington, DC, 1993.
15. M. Clegg, J. Edmonds, and R. Impagliazzo. Using the Gröbner basis algorithm to find proofs of unsatisfiability. In 28th STOC, pages 174-183, Philadelphia, PA, May 1996.
16. B. Cha and K. Iwama. Adding new clauses for faster local search. In 13th AAAI, pages 332-337, Portland, OR, August 1996.
17. P. Cheeseman, B. Kenefsky, and W. M. Taylor. Where the really hard problems are. In Proceedings of IJCAI-91, pages 331-337. Morgan Kaufmann, 1991.
18. S. Cook and D. Mitchell. Finding hard instances of the satisfiability problem: a survey. In DIMACS Series in Discr. Math. and Theoretical Comp. Sci., volume 35, pages 1-17. American Math. Society, 1997.
19. V. Chv́atal and B. Reed. Mick gets some (the odds are on his side). In 33rd FOCS, pages 620-627, Pittsburgh, PA, October 1992. IEEE.
20. V. Chv́atal and E. Szemeŕedi. Many hard examples for resolution. J. Assoc. Comput. Mach., 35(4):759-768, 1988.
21. O. Dubois, Y. Boufkhad, and J. Mandler. Typical random 3-SAT formulae and the satisfiability threshold. Technical Report 7, ECCC, 2003.
22. E. Dantsin, A. Goerdt, E. A. Hirsch, R. Kannan, J. M. Kleinberg, C. H. Papadimitriou, P. Raghavan, and U. Schöning. A deterministic (2 - 2/(k + 1))n algorithm for k-SAT based on local search. Theoretical Comput. Sci., 289(1):69-83, 2002.
23. S. Droste, T. Jansen, and I. Wegener. On the analysis of the (1+1) evolutionary algorithm. Theoretical Comput. Sci., 276(1-2):51-81, 2002.
24. A. E. Eiben and J. E. Smith. Introduction to Evolutionary Computing. springer, 2003.
25. J. Frank, P. Cheeseman, and J. Stutz. Where gravity fails: Local search topology. JAIR, 7:249-281, 1997.
26. J. Franco and M. Paull. Probabilistic analysis of the Davis-Putnam procedure for solving the satisfiability problem. Discr. Applied Mathematics, 5:77-87, 1983.
27. J. Franco. Probabilistic analysis of the pure literal heuristic for the satisfiability problem. Annals of Operations Research, 1:273-289, 1983.
28. J. Frank. Learning short-term weights for GSAT. In 15th IJCAI, pages 384-391, Nagoya, Japan, August 1997.
29. E. Friedgut. Sharp thresholds of graph properties, and the k-sat problem. Journal of the American Mathematical Society, 12:1017-1054, 1999.
30. A. Frieze and S. Suen. Analysis of two simple heuristics on a random instance of k-SAT. J. Alg., 20(2):312-355, 1996.
31. O.-C. Granmo and N. Bouhmala. Solving the satisfiability problem using finite learning automata. Intl. J. Comp. Sci. App., 4(3):15-29, 2007.
32. M. L. Ginsberg and D. A. McAllester. GSAT and dynamic backtracking. In 4th KR, pages 226-237, Bonn, Germany, May 1994.
33. J. Gottlieb, E. Marchiori, and C. Rossi. Evolutionary algorithms for the satisfiability problem. Evolutionary Computation, 10(1):35-50, 2002.
34. A. Goldberg. On the complexity of the satisfiability problem. Technical Report Report No. 16, Courant Computer Science, New York University, 1979.
35. J. Gu, P. W. Purdom, J. Franco, and B. W. Wah. Algorithms for the Satisfiability (SAT) Problem: A Survey. In Satisfiability (SAT) Problem, DIMACS, pages 19-151. American Mathematical Society, 1997.
36. C. P. Gomes and B. Selman. Can get satisfaction. Nature, 435:751-752, 2005.
37. J. Gu. Efficient local search for very large-scale satisfiability problems. Sigart Bulletin, 3(1):8-12, 1992.
38. I. P. Gent and T. Walsh. Towards an understanding of hill-climbing procedures for SAT. In 11th AAAI, pages 28-33, Washington, DC, July 1993.
39. A. Haken. The intractability of resolution. Theoretical Comput. Sci., 39:297-305, 1985.
40. E. A. Hirsch and A. Kojevnikov. UnitWalk: A new SAT solver that uses local search guided by unit clause elimination. Annals Math. and AI, 43(1):91-111, 2005.
41. D. Habet, C. M. Li, L. Devendeville, and M. Vasquez. A hybrid approach for SAT. In 8th CP, volume 2470 of LNCS, pages 172- 184, Ithaca, NY, September 2002.
42. J. N. Hooker. A quantitative approach to logical inference. Decision Support Systems, 4:45-69, 1988.
43. H. H. Hoos. On the run-time behaviour of stochastic local search algorithms for SAT. In Proceedings of AAAI-99, pages 661-666. AAAI Press, 1999.
44. H. H. Hoos. An adaptive noise mechanism for WalkSAT. In 18th AAAI, pages 655-660, Edmonton, Canada, July 2002.
45. M. Hajiaghayi and G. B. Sorkin. The satisability threshold of random 3-SAT is at least 3.52. Technical Report RC22942, IBM Research Report, 2003. http://arxiv.org/pdf/math.CO/0310193.
46. H. H. Hoos and T. Stützle. Stochastic Local Search: Foundations and Applications. Morgan Kaufmann, San Francisco, CA, 2004.
47. F. Hutter, D. A. D. Tompkins, and H. H. Hoos. Scaling and probabilistic smoothing: Efficient dynamic local search for SAT. In 8th CP, volume 2470 of LNCS, pages 233-248, Ithaca, NY, September 2002.
48. A. Ishtaiwi, J. Thornton, Anbulagan, A. Sattar, and D. N. Pham. Adaptive clause weight redistribution. In 12th CP, volume 4204 of LNCS, pages 229-243, Nantes, France, September 2006.
49. D. S. Johnson, C. R. Aragon, L. A. McGeoch, and C. Schevon. Optimization by simulated annealing: an experimental evaluation; part II. Operations Research, 39, 1991.
50. S. Janson, Y. C. Stamatiou, and M. Vamvakari. Bounding the unsatisfiability threshold of random 3-SAT. Random Struct. and Alg., 17(2):103-116, 2000.
51. D. S. Johnson and M. A. Trick, editors. Cliques, Coloring and Satisfiability: the Second DIMACS Implementation Challenge, volume 26 of DIMACS Series in DMTCS. Amer. Math. Soc., 1996.
52. S. Kirkpatrick, D. Gelatt Jr., and M. P. Vecchi. Optimization by simuleated annealing. Science, 220(4598):671-680, 1983.
53. L. M. Kirousis, E. Kranakis, and D. Krizanc. Approximating the unsatisfiability threshold of random formulas. In Proceedings of the Fourth Annual European Symposium on Algorithms, pages 27-38, Barcelona, Spain, September 1996.
54. A. C. Kaporis, L. M. Kirousis, and E. G. Lalas. The probabilistic analysis of a greedy satisfiability algorithm. Random Structures and Algorithms, 28(4):444-480, 2006.
55. A. Kamath, N. Karmarkar, K. Ramakrishnan, and M. Resende. Computational experience with an interior point algorithm on the satisfiability problem. In Proceedings of Integer Programming and Combinatorial Optimization, pages 333-349, Waterloo, Canada, 1990. Mathematical Programming Society.
56. F. Krzakala, A. Montanari, F. Ricci-Tersenghi, G. Semerjian, and L. Zdeborova. Gibbs states and the set of solutions of random constraint satisfaction problems. PNAS, 104(25):10318-10323, June 2007.
57. K. Konolige. Easy to be hard: Difficult problems for greedy algorithms. In 4th KR, pages 374-378, Bonn, Germany, May 1994.
58. S. Kirkpatrick and B. Selman. Critical behavior in the satisfiability of random Boolean expressions. Science, 264:1297-1301, May 1994. Also p. 1249: "Math. Logic: Pinning Down a Trecherous Border in Logical Statements" by B. Cipra.
59. L. Kroc, A. Sabharwal, and B. Selman. Survey propagation revisited. In 23rd UAI, pages 217-226, Vancouver, BC, July 2007.
60. L. Kroc, A. Sabharwal, and B. Selman. Leveraging belief propagation, backtrack search, and statistics for model counting. In 5th CPAIOR, volume 5015 of LNCS, pages 127-141, Paris, France, May 2008.
61. S. Lin and B. W. Kernighan. An efficient heuristic algorithm for the traveling-salesman problem. Operations Research, 21:498-516, 1973.
62. X. Y. Li, M. F. M. Stallmann, and F. Brglez. QingTing: A local search SAT solver using an effective switching strategy and an efficient unit propagation. In 6th SAT, pages 53-68, Santa Margherita, Italy, May 2003.
63. F. Lardeux, F. Saubion, and J.-K. Hao. GASAT: A genetic local search algorithm for the satisfiability problem. Evolutionary Computation, 14(2):223-253, 2006.
64. C. M. Li, W. Wei, and H. Zhang. Combining adaptive noise and look-ahead in local search for SAT. In 10th SAT, volume 4501 of LNCS, pages 121-133, Lisbon, Portugal, May 2007.
65. E. Maneva. Belief Propagation Algorithms for Constraint Satisfaction Problems. PhD thesis, University of California, Berkeley, 2006.
66. S. Minton, M. D. Johnston, A. B. Philips, and P. Laird. Solving large-scale constraint satisfaction an scheduling problems using a heuristic repair method. In Proceedings AAAI-90, pages 17-24. AAAI Press, 1990.
67. E. Maneva, E. Mossel, and M. J. Wainwright. A new look at survey propagation and its generalizations. J. Assoc. Comput. Mach., 54(4):17, July 2007.
68. M. Ḿezard, T. Mora, and R. Zecchina. Clustering of solutions in the random satisfiability problem. Phy. Rev. Lett., 94:197205, May 2005.
69. S. Mertens, M. Ḿezard, and R. Zecchina. Threshold values of random K-SAT from the cavity method. Random Struct. and Alg., 28(3):340-373, 2006.
70. P. Morris. The breakout method for escaping from local minima. In 11th AAAI, pages 428-433, Washington, DC, July 1993.
71. M. Ḿezard, G. Parisi, and R. Zecchina. Analytic and algorithmic solution of random satisfiability problems. Science, 297(5582):812-815, 2002.
72. E. Maneva and A. Sinclair. On the satisfiability threshold and survey propagation for random 3-SAT, 2007. http://arxiv.org/abs/cs.CC/0609072.
73. B. Mazure, L. Sais, and E. Gregoire. Boosting complete techniques thanks to local search methods. In Proc. Math and AI, 1996.
74. B. Mazure, L. Sais, and E. Gŕegoire. Tabu search for SAT. In 14th AAAI, pages 281-285, Providence, RI, July 1997.
75. D. A. McAllester, B. Selman, and H. Kautz. Evidence for invariants in local search. In AAAI/IAAI, pages 321-326, Providence, RI, July 1997.
76. D. Mitchell, B. Selman, and H. J. Levesque. Hard and easy distributions of SAT problems. In Proc. AAAI-92, pages 459-465, San Jose, CA, 1992.
77. M. Ḿezard and R. Zecchina. Random k-satisfiability problem: From an analytic solution to an efficient algorithm. Phy. Rev. E, 66:056126, November 2002.
78. R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, and L. Troyansky. Determining computational complexity from characteristic phase transitions. Nature, 400(8):133-137, 1999.
79. C. H. Papadimitriou. On selecting a satisfying truth assignment. In 32nd FOCS, pages 163-169, San Juan, Puerto Rico, October 1991. IEEE.
80. P. W. Purdom Jr. and C. A. Brown. Polynomial average-time satisfiability problems. Information Science, 41:23-42, 1987.
81. J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, 1988.
82. S. D. Prestwich. Local search and backtracking vs non-systematic backtracking. In AAAI 2001 Fall Symp. on Using Uncertainty within Computation, 2001.
83. S. D. Prestwich. Variable dependency in local search: Prevention is better than cure. In 10th SAT, Lisbon, Portugal, May 2007.
84. C. H. Papadimitriou and K. Steiglitz. Combinatorial Optimization. Prentice-Hall, Inc., 1982.
85. D. N. Pham, J. Thornton, and A. Sattar. Building structure into local search for SAT. In 20th IJCAI, pages 2359-2364, Hyderabad, India, January 2007.
86. A. J. Parkes and J. P. Walser. Tuning local search for satisfiability testing. In 13th AAAI, pages 356-362, Portland, OR, August 1996.
87. I. Rish and R. Dechter. To guess or to think? hybrid algorithms for SAT. In Proc. Conference on Principles of Constraint Programming (CP-96), pages 555-556, 1996.
88. M. G. C. Resende and T. A. Feo. A GRASP for satisfiability. In Johnson and Trick [JT96], pages 499-520.
89. S. Seitz, M. Alava, and P. Orponen. Focused local search for random 3-satisfiability. J. Stat. Mech., P06006, 2005.
90. U. Schöning. A probabilistic algorithm for k-SAT and constraint satisfaction problems. In 40th FOCS, pages 410-414, New York, NY, October 1999. IEEE.
91. U. Schöning. A probabilistic algorithm for k-SAT based on limited local search and restart. Algorithmica, 32(4):615-623, 2002.
92. B. Selman and H. A. Kautz. Domain-independent extensions to GSAT: Solving large structured satisfiability problems. In 13th IJCAI, pages 290-295, France, 1993.
93. B. Selman and S. Kirkpatrick. Critical behavior in the computational cost of satisfiability testing. AI J., 81:273-295, 1996.
94. B. Selman, H. Kautz, and B. Cohen. Noise strategies for local search. In Proc. AAAI-94, pages 337-343, Seattle, WA, 1994.
95. B. Selman, H. Kautz, and B. Cohen. Local search strategies for satisfiability testing. In Johnson and Trick [JT96], pages 521-532.
96. B. Selman, H. J. Levesque, and D. G. Mitchell. A new method for solving hard satisfiability problems. In 10th AAAI, pages 440-446, San Jose, CA, July 1992.
97. W. M. Spears. Simulated annealing for hard satisfiability problems. In Johnson and Trick [JT96], pages 533-558.
98. D. Schuurmans and F. Southey. Local search characteristics of incomplete SAT procedures. AI J., 132(2):121-150, 2001.
99. D. Schuurmans, F. Southey, and R. C. Holte. The exponentiated subgradient algorithm for heuristic boolean programming. In 17th IJCAI, pages 334-341, Seattle, WA, August 2001.
100. Y. Shang and B.W.Wah. A discrete Lagrangian-based global-search method for solving satisfiability problems. J. of Global Optimization, 12(1):61-99, 1998.
101. J. Thornton, D. N. Pham, S. Bain, and V. Ferreira Jr. Additive versus multiplicative clause weighting for SAT. In 19th AAAI, pages 191-196, San Jose, CA, July 2004.
102. Z. Wu and B. W. Wah. Trap escaping strategies in discrete Lagrangian methods for solving hard satisfiability and maximum satisfiability problems. In 16th AAAI, pages 673-678, Orlando, FL, July 1999.
103. Z.Wu and B.W.Wah. An efficient global-search strategy in discrete Lagrangian methods for solving hard satisfiability problems. In 17th AAAI, pages 310-315, Austin, TX, July 2000.
104. L. Zdeborova and F. Krzakala. Phase transition in the coloring of random graphs. Phy. Rev. E, 76:031131, September 2007.