Computational experience with an interior point algorithm on the satisfiability problem

We apply the zero-one integer programming algorithm described in Karmarkar [12] and Karmarkar, Resende and Ramakrishnan [13] to solve randomly generated instances of the satisfiability problem (SAT). The interior point algorithm is briefly reviewed and shown to be easily adapted to solve large instances of SAT. Hundreds of instances of SAT (having from 100 to 1000 variables and 100 to 32,000 clauses) are randomly generated and solved. For comparison, we attempt to solve the problems via linear programming relaxation with MINOS.

[1]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[2]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[3]  Mauricio G. C. Resende,et al.  An interior point algorithm to solve computationally difficult set covering problems , 1991, Math. Program..

[4]  J. Hooker.  Resolution vs. cutting plane solution of inference problems: Some computational experience , 1988 .

[5]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[6]  Michael A. Saunders,et al.  MINOS 5. 0 user's guide , 1983 .

[7]  John N. Hooker,et al.  A quantitative approach to logical inference , 1988, Decis. Support Syst..

[8]  Sartaj Sahni,et al.  Computationally Related Problems , 1974, SIAM J. Comput..

[9]  Ronald R. Yager,et al.  A Mathematical Programming Approach to Inference with the Capability of Implementing Default Rules , 1988, Int. J. Man Mach. Stud..

[10]  H. P. Williams.  Linear and integer programming applied to the propositional calculus , 1987 .

[11]  Panos M. Pardalos,et al.  Modeling and integer programming techniques applied to propositional calculus , 1990, Comput. Oper. Res..

[12]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[13]  Nils J. Nilsson,et al.  Principles of Artificial Intelligence , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  H. P. Williams.  Logical problems and integer programming , 1977 .

[15]  Narendra Karmarkar,et al.  An Interior-Point Approach to NP-Complete Problems , 1990, Conference on Integer Programming and Combinatorial Optimization.

[16]  Pierre Hansen,et al.  A linear expected-time algorithm for deriving all logical conclusions implied by a set of boolean inequalities , 1986, Math. Program..

[17]  John N. Hooker,et al.  Generalized resolution and cutting planes , 1988 .

[18]  J. K. Lowe,et al.  Some results and experiments in programming techniques for propositional logic , 1986, Comput. Oper. Res..

[19]  Robert G. Jeroslow,et al.  Computation-oriented reductions of predicate to propositional logic , 1988, Decis. Support Syst..

[20]  R. R. Yager.  A mathematical programming approach to inference with the capability to implement default rules , 1990 .