A solution scheme of satisfiability problem by active usage of totally unimodularity property.

by Mei Long.Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.Includes bibliographical references (leaves 93-98).Abstracts in English and Chinese.Table of Contents --- p.vAbstract --- p.viiiAcknowledgements --- p.xChapter 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 --- Satisfiability Problem --- p.4Chapter 2.1 --- Satisfiability Problem --- p.5Chapter 2.1.1 --- Basic Definition --- p.5Chapter 2.1.2 --- Phase Transitions --- p.5Chapter 2.2 --- History --- p.6Chapter 2.3 --- The Basic Search Algorithm --- p.8Chapter 2.4 --- Some Improvements to the Basic Algorithm --- p.9Chapter 2.4.1 --- Satz by Chu-Min Li --- p.9Chapter 2.4.2 --- Heuristics and Local Search --- p.12Chapter 2.4.3 --- Relaxation --- p.13Chapter 2.5 --- Benchmarks --- p.14Chapter 2.5.1 --- Specific Problems --- p.14Chapter 2.5.2 --- Randomly Generated Problems --- p.14Chapter 2.6 --- Software and Internet Information for SAT solving --- p.16Chapter 2.6.1 --- Stochastic Local Search Algorithms (incomplete) --- p.16Chapter 2.6.2 --- Systematic Search Algorithms (complete) --- p.16Chapter 2.6.3 --- Some useful Links to SAT Related Sites --- p.17Chapter 3 --- Integer Programming Formulation for Logic Problem --- p.18Chapter 3.1 --- SAT Problem --- p.19Chapter 3.2 --- MAXSAT Problem --- p.19Chapter 3.3 --- Logical Inference Problem --- p.19Chapter 3.4 --- Weighted Exact Satisfiability Problem --- p.20Chapter 4 --- Integer Programming Formulation for SAT Problem --- p.22Chapter 4.1 --- From 3-CNF SAT Clauses to Zero-One IP Constraints --- p.22Chapter 4.2 --- Integer Programming Model for 3-SAT --- p.23Chapter 4.3 --- The Equivalence of the SAT and the IP --- p.23Chapter 4.4 --- Example --- p.24Chapter 5 --- Integer Solvability of Linear Programs --- p.27Chapter 5.1 --- Unimodularity --- p.27Chapter 5.2 --- Totally Unimodularity --- p.28Chapter 5.3 --- Some Results on Recognition of Linear Solvability of IP --- p.32Chapter 6 --- TU Based Matrix Research Results --- p.33Chapter 6.1 --- 2x2 Matrix's TU Property --- p.33Chapter 6.2 --- Extended Integer Programming Model for SAT --- p.34Chapter 6.3 --- 3x3 Matrix's TU Property --- p.35Chapter 7 --- Totally Unimodularity Based Branching-and-Bound Algorithm --- p.38Chapter 7.1 --- Introduction --- p.38Chapter 7.1.1 --- Enumeration Trees --- p.39Chapter 7.1.2 --- The Concept of Branch and Bound --- p.42Chapter 7.2 --- TU Based Branching Rule --- p.43Chapter 7.2.1 --- How to sort variables based on 2x2 submatrices --- p.43Chapter 7.2.2 --- How to sort the rest variables --- p.45Chapter 7.3 --- TU Based Bounding Rule --- p.46Chapter 7.4 --- TU Based Branch-and-Bound Algorithm --- p.47Chapter 7.5 --- Example --- p.49Chapter 8 --- Numerical Result --- p.57Chapter 8.1 --- Experimental Result --- p.57Chapter 8.2 --- Statistical Results of ILOG CPLEX --- p.59Chapter 9 --- Conclusions --- p.61Chapter 9.1 --- Contributions --- p.61Chapter 9.2 --- Future Work --- p.62Chapter A --- The Coefficient Matrix A for Example in Chapter 7 --- p.64Chapter B --- The Detailed Numerical Information of Solution Process for Exam- ple in Chapter 7 --- p.66Chapter C --- Experimental Result --- p.67Chapter C.1 --- "# of variables: 20, # of clauses: 91" --- p.67Chapter C.2 --- "# of variables: 50, # of clauses: 218" --- p.70Chapter C.3 --- # of variables: 75，# of clauses: 325 --- p.73Chapter C.4 --- "# of variables: 100, # of clauses: 430" --- p.76Chapter D --- Experimental Result of ILOG CPLEX --- p.80Chapter D.1 --- # of variables: 20´ة # of clauses: 91 --- p.80Chapter D.2 --- # of variables: 50，#of clauses: 218 --- p.83Chapter D.3 --- # of variables: 75，# of clauses: 325 --- p.86Chapter D.4 --- "# of variables: 100, # of clauses: 430" --- p.89Bibliography --- p.9