An integer programming approach for the satisfiability problems.

by Lui Oi Lun Irene.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.Includes bibliographical references (leaves 128-132).Abstracts in English and Chinese.List of Figures --- p.viiList of Tables --- p.viiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Satisfiability Problem --- p.1Chapter 1.2 --- Motivation of the Research --- p.1Chapter 1.3 --- Overview of the Thesis --- p.2Chapter 2 --- Constraint Satisfaction Problem and Satisfiability Problem --- p.4Chapter 2.1 --- Constraint Programming --- p.4Chapter 2.2 --- Satisfiability Problem --- p.6Chapter 2.3 --- Methods in Solving SAT problem --- p.7Chapter 2.3.1 --- Davis-Putnam-Loveland Procedure --- p.7Chapter 2.3.2 --- SATZ by Chu-Min Li --- p.8Chapter 2.3.3 --- Local Search for SAT --- p.11Chapter 2.3.4 --- Integer Linear Programming Method for SAT --- p.12Chapter 2.3.5 --- Semidefinite Programming Method --- p.13Chapter 2.4 --- Softwares for SAT --- p.15Chapter 2.4.1 --- SAT01 --- p.15Chapter 2.4.2 --- "SATZ and SATZ213, contributed by Chu-Min Li" --- p.15Chapter 2.4.3 --- Others --- p.15Chapter 3 --- Integer Programming --- p.17Chapter 3.1 --- Introduction --- p.17Chapter 3.1.1 --- Formulation of IPs and BIPs --- p.18Chapter 3.1.2 --- Binary Search Tree --- p.19Chapter 3.2 --- Methods in Solving IP problem --- p.19Chapter 3.2.1 --- Branch-and-Bound Method --- p.20Chapter 3.2.2 --- Cutting-Plane Method --- p.23Chapter 3.2.3 --- Duality in Integer Programming --- p.26Chapter 3.2.4 --- Heuristic Algorithm --- p.28Chapter 3.3 --- Zero-one Optimization and Continuous Relaxation --- p.29Chapter 3.3.1 --- Introduction --- p.29Chapter 3.3.2 --- The Roof Dual expressed in terms of Lagrangian Relaxation --- p.30Chapter 3.3.3 --- Determining the Existence of a Duality Gap --- p.31Chapter 3.4 --- Software for solving Integer Programs --- p.33Chapter 4 --- Integer Programming Formulation for SAT Problem --- p.35Chapter 4.1 --- From 3-CNF SAT Clauses to Zero-One IP Constraints --- p.35Chapter 4.2 --- From m-Constrained IP Problem to Singly-Constrained IP Problem --- p.38Chapter 4.2.1 --- Example --- p.39Chapter 5 --- A Basic Branch-and-Bound Algorithm for the Zero-One Polynomial Maximization Problem --- p.42Chapter 5.1 --- Reason for choosing Branch-and-Bound Method --- p.42Chapter 5.2 --- Searching Algorithm --- p.43Chapter 5.2.1 --- Branch Rule --- p.44Chapter 5.2.2 --- Bounding Rule --- p.46Chapter 5.2.3 --- Fathoming Test --- p.46Chapter 5.2.4 --- Example --- p.47Chapter 6 --- Revised Bound Rule for Branch-and-Bound Algorithm --- p.55Chapter 6.1 --- Revised Bound Rule --- p.55Chapter 6.1.1 --- CPLEX --- p.57Chapter 6.2 --- Example --- p.57Chapter 6.3 --- Conclusion --- p.65Chapter 7 --- Revised Branch Rule for Branch-and-Bound Algorithm --- p.67Chapter 7.1 --- Revised Branch Rule --- p.67Chapter 7.2 --- Comparison between Branch Rule and Revised Branch Rule --- p.69Chapter 7.3 --- Example --- p.72Chapter 7.4 --- Conclusion --- p.73Chapter 8 --- Experimental Results and Analysis --- p.80Chapter 8.1 --- Experimental Results --- p.80Chapter 8.2 --- Statistical Analysis --- p.33Chapter 8.2.1 --- Analysis of Search Techniques --- p.83Chapter 8.2.2 --- Discussion of the Performance of SATZ --- p.85Chapter 9 --- Concluding Remarks --- p.87Chapter 9.1 --- Conclusion --- p.87Chapter 9.2 --- Suggestions for Future Research --- p.88Chapter A --- Searching Procedures for Solving Constraint Satisfaction Problem (CSP) --- p.91Chapter A.1 --- Notation --- p.91Chapter A.2 --- Procedures for Solving CSP --- p.92Chapter A.2.1 --- Generate and Test --- p.92Chapter A.2.2 --- Standard Backtracking --- p.93Chapter A.2.3 --- Forward Checking --- p.94Chapter A.2.4 --- Looking Ahead --- p.95Chapter B --- Complete Results for Experiments --- p.96Chapter B.1 --- Complete Result for SATZ --- p.96Chapter B.1.1 --- n =5 --- p.95Chapter B.1.2 --- n = 10 --- p.98Chapter B.1.3 --- n = 30 --- p.99Chapter B.2 --- Complete Result for Basic Branch-and-Bound Algorithm --- p.101Chapter B.2.1 --- n二5 --- p.101Chapter B.2.2 --- n = 10 --- p.104Chapter B.2.3 --- n = 30 --- p.107Chapter B.3 --- Complete Result for Revised Bound Rule --- p.109Chapter B.3.1 --- n = 5 --- p.109Chapter B.3.2 --- n = 10 --- p.112Chapter B.3.3 --- n = 30 --- p.115Chapter B.4 --- Complete Result for Revised Branch-and-Bound Algorithm --- p.118Chapter B.4.1 --- n = 5 --- p.118Chapter B.4.2 --- n = 10 --- p.121Chapter B.4.3 --- n = 30 --- p.124Bibliography --- p.12

Maximum Renamable Horn Sub-CNFs

The NP-hard problem of finding the largest renamable Horn sub-CNF of a given CNF is considered, and a polynomial time approximation algorithm is presented for this problem. It is shown that for cubic CNFs this algorithm has a guaranteed performance ratio of 40 67