Return to search

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.v / Abstract --- p.viii / Acknowledgements --- p.x / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Satisfiability Problem --- p.1 / Chapter 1.2 --- Motivation of the Research --- p.1 / Chapter 1.3 --- Overview of the Thesis --- p.2 / Chapter 2 --- Satisfiability Problem --- p.4 / Chapter 2.1 --- Satisfiability Problem --- p.5 / Chapter 2.1.1 --- Basic Definition --- p.5 / Chapter 2.1.2 --- Phase Transitions --- p.5 / Chapter 2.2 --- History --- p.6 / Chapter 2.3 --- The Basic Search Algorithm --- p.8 / Chapter 2.4 --- Some Improvements to the Basic Algorithm --- p.9 / Chapter 2.4.1 --- Satz by Chu-Min Li --- p.9 / Chapter 2.4.2 --- Heuristics and Local Search --- p.12 / Chapter 2.4.3 --- Relaxation --- p.13 / Chapter 2.5 --- Benchmarks --- p.14 / Chapter 2.5.1 --- Specific Problems --- p.14 / Chapter 2.5.2 --- Randomly Generated Problems --- p.14 / Chapter 2.6 --- Software and Internet Information for SAT solving --- p.16 / Chapter 2.6.1 --- Stochastic Local Search Algorithms (incomplete) --- p.16 / Chapter 2.6.2 --- Systematic Search Algorithms (complete) --- p.16 / Chapter 2.6.3 --- Some useful Links to SAT Related Sites --- p.17 / Chapter 3 --- Integer Programming Formulation for Logic Problem --- p.18 / Chapter 3.1 --- SAT Problem --- p.19 / Chapter 3.2 --- MAXSAT Problem --- p.19 / Chapter 3.3 --- Logical Inference Problem --- p.19 / Chapter 3.4 --- Weighted Exact Satisfiability Problem --- p.20 / Chapter 4 --- Integer Programming Formulation for SAT Problem --- p.22 / Chapter 4.1 --- From 3-CNF SAT Clauses to Zero-One IP Constraints --- p.22 / Chapter 4.2 --- Integer Programming Model for 3-SAT --- p.23 / Chapter 4.3 --- The Equivalence of the SAT and the IP --- p.23 / Chapter 4.4 --- Example --- p.24 / Chapter 5 --- Integer Solvability of Linear Programs --- p.27 / Chapter 5.1 --- Unimodularity --- p.27 / Chapter 5.2 --- Totally Unimodularity --- p.28 / Chapter 5.3 --- Some Results on Recognition of Linear Solvability of IP --- p.32 / Chapter 6 --- TU Based Matrix Research Results --- p.33 / Chapter 6.1 --- 2x2 Matrix's TU Property --- p.33 / Chapter 6.2 --- Extended Integer Programming Model for SAT --- p.34 / Chapter 6.3 --- 3x3 Matrix's TU Property --- p.35 / Chapter 7 --- Totally Unimodularity Based Branching-and-Bound Algorithm --- p.38 / Chapter 7.1 --- Introduction --- p.38 / Chapter 7.1.1 --- Enumeration Trees --- p.39 / Chapter 7.1.2 --- The Concept of Branch and Bound --- p.42 / Chapter 7.2 --- TU Based Branching Rule --- p.43 / Chapter 7.2.1 --- How to sort variables based on 2x2 submatrices --- p.43 / Chapter 7.2.2 --- How to sort the rest variables --- p.45 / Chapter 7.3 --- TU Based Bounding Rule --- p.46 / Chapter 7.4 --- TU Based Branch-and-Bound Algorithm --- p.47 / Chapter 7.5 --- Example --- p.49 / Chapter 8 --- Numerical Result --- p.57 / Chapter 8.1 --- Experimental Result --- p.57 / Chapter 8.2 --- Statistical Results of ILOG CPLEX --- p.59 / Chapter 9 --- Conclusions --- p.61 / Chapter 9.1 --- Contributions --- p.61 / Chapter 9.2 --- Future Work --- p.62 / Chapter A --- The Coefficient Matrix A for Example in Chapter 7 --- p.64 / Chapter B --- The Detailed Numerical Information of Solution Process for Exam- ple in Chapter 7 --- p.66 / Chapter C --- Experimental Result --- p.67 / Chapter C.1 --- "# of variables: 20, # of clauses: 91" --- p.67 / Chapter C.2 --- "# of variables: 50, # of clauses: 218" --- p.70 / Chapter C.3 --- # of variables: 75,# of clauses: 325 --- p.73 / Chapter C.4 --- "# of variables: 100, # of clauses: 430" --- p.76 / Chapter D --- Experimental Result of ILOG CPLEX --- p.80 / Chapter D.1 --- # of variables: 20´ة # of clauses: 91 --- p.80 / Chapter D.2 --- # of variables: 50,#of clauses: 218 --- p.83 / Chapter D.3 --- # of variables: 75,# of clauses: 325 --- p.86 / Chapter D.4 --- "# of variables: 100, # of clauses: 430" --- p.89 / Bibliography --- p.93

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_324366
Date January 2003
ContributorsLong, Mei., Chinese University of Hong Kong Graduate School. Division of Systems Engineering and Engineering Management.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, x, 98 leaves : ill. ; 30 cm.
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Page generated in 0.0015 seconds