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020 _a9781394235940
020 _a139423595X
_qelectronic book
020 _a1394235968
_qelectronic book
020 _a1394235976
_qelectronic book
020 _a9781394235957
_qelectronic book
020 _a9781394235964
_qelectronic book
020 _a9781394235971
_qelectronic book
020 _z9781394235940
_qhardcover
035 _a(OCoLC)1429725364
040 _aDLC
_beng
_erda
_cDLC
_dOCLCO
_dYDX
_dDG1
_dUKAHL
041 _aeng
042 _apcc
050 0 4 _aQA164
_b.A4693 2024
082 0 0 _a511/.6
_223/eng/20240412
100 1 _aAlzalg, Baha,
_0https://id.loc.gov/authorities/names/n2024013890
_eauthor.
245 1 0 _aCombinatorial and algorithmic mathematics :
_bfrom foundation to optimization /
_cBaha Alzalg, the University of Jordan, Amman, Jordan.
264 1 _aHoboken, NJ :
_bWiley,
_c2024.
264 4 _c©2024.
300 _a1 online resource (xxi, 506 pages) :
_billustrations (chiefly color)
336 _atext
_btxt
_2rdacontent.
337 _acomputer
_bc
_2rdamedia.
338 _aonline resource
_bcr
_2rdacarrier.
340 _2rdacc
_0http://rdaregistry.info/termList/RDAColourContent/1003.
504 _aIncludes bibliographical references and index.
505 0 _aTable of Contents About the Author xiii Preface xv Acknowledgments xvii About the Companion Website xxi Part I Foundations 1 1 Mathematical Logic 3 1.1 Propositions 3 1.2 Logical Operators 6 1.3 Propositional Formulas 15 1.4 Logical Normal Forms 24 1.5 The Boolean Satisfiability Problem 29 1.6 Predicates and Quantifiers 30 1.7 Symbolizing Statements of the Form "All P Are Q" 37 2 Set-Theoretic Structures 51 2.1 Induction 51 2.2 Sets 54 2.3 Relations 59 2.4 Partitions 64 2.5 Functions 65 3 Analytic and Algebraic Structures 77 3.1 Sequences 77 3.2 Summations and Series 81 3.3 Matrices, Subspaces, and Bases 87 3.4 Convexity, Polyhedra, and Cones 91 3.5 Farkas' Lemma and Its Variants 95 Part II Combinatorics 103 4 Graphs105 4.1 Basic Graph Definitions 106 4.2 Isomorphism and Properties of Graphs 113 4.3 Eulerian and Hamiltonian Graphs 118 4.4 Graph Coloring 122 4.5 Directed Graphs 125 5 Recurrences 133 5.1 Guess-and-Confirm 133 5.2 Recursion-Iteration 136 5.3 Generating Functions 138 5.4 Recursion-Tree 140 6 Counting149 6.1 Binomial Coefficients and Identities 149 6.2 Fundamental Principles of Counting 154 6.3 The Pigeonhole Principle 161 6.4 Permutations 163 6.5 Combinations 166 Part III Algorithms 179 7 Analysis of Algorithms 181 7.1 Constructing and Comparing Algorithms 182 7.2 Running Time of Algorithms 189 7.3 Asymptotic Notation 199 7.4 Analyzing Decision-Making Statements 211 7.5 Analyzing ProgramsWithout Function Calls 213 7.6 Analyzing Programs with Function Calls 219 7.7 The Complexity Class NP-Complete 224 8 Array and Numeric Algorithms 241 8.1 Array Multiplication Algorithms 241 8.2 Array Searching Algorithms 244 8.3 Array Sorting Algorithms 248 8.4 Euclid's Algorithm 253 8.5 Newton's Method Algorithm 255 9 Elementary Combinatorial Algorithms 267 9.1 Graph Representations 267 9.2 Breadth-First Search Algorithm 270 9.3 Applications of Breadth-First Search 273 9.4 Depth-First Search Algorithm 277 9.5 Applications of Depth-First Search 279 9.6 Topological Sort 283 Part IV Optimization 293 10 Linear Programming 295 10.1 Linear Programming Formulation and Examples 296 10.2 The Graphical Method 302 10.3 Standard Form Linear Programs 309 10.4 Geometry of Linear Programming 311 10.5 The Simplex Method 320 10.6 Duality in Linear Programming 339 10.7 A Homogeneous Interior-Point Method 347 11 Second-Order Cone Programming 363 11.1 The Second-Order Cone and Its Algebraic Structure 363 11.2 Second-Order Cone Programming Formulation 368 11.3 Applications in Engineering and Finance 370 11.4 Duality in Second-Order Cone Programming 375 11.5 A Primal-Dual Path-Following Algorithm 379 11.6 A Homogeneous Self-Dual Algorithm 386 12 Semidefinite Programming and Combinatorial Optimization 395 12.1 The Cone of Positive Semidefinite Matrices 395 12.2 Semidefinite Programming Formulation 399 12.3 Applications in Combinatorial Optimization 401 12.4 Duality in Semidefinite Programming 405 12.5 A Primal–Dual Path-Following Algorithm 408 Exercises 417 Notes and Sources 418 References 418 Appendix A Solutions to Chapter Exercises 421 References 487 Bibliography 489 Index 501
520 _a"Throughout operations research, computer science and pure and applied mathematics, combinatorics problems arise frequently, where the solution is to find the "optimal" object from a finite set of mathematical objects. Typically, it is impractical to search exhaustively for all possible solutions. The development of efficient algorithms for exploring the solution space is known as combinatorial optimisation. Many problems, such as network optimisation, supply chain management, data compression, resource allocation and game theory - indeed most of machine learning, AI, and current high profile computer science topics rely on optimisation. Together, combinatorial and algorithmic mathematics provide powerful tools for solving these real-world problems, and for in-demand subjects such as data science, machine learning, and artificial intelligence, a unified knowledge of discrete structures, algorithms and combinatorial optimization is considered essential"--
_cProvided by publisher.
545 0 _aAbout the Author Baha Alzalg is a Professor in the Department of Mathematics at the University of Jordan in Amman, Jordan. He has also held the post of visiting associate professor in the Department of Computer Science and Engineering at the Ohio State University in Columbus, Ohio. His research interests include topics in optimization theory, applications, and algorithms, with an emphasis on interior-point methods for cone programming.
650 0 _aAlgorithms.
_0https://id.loc.gov/authorities/subjects/sh85003487.
650 0 _aCombinatorial analysis.
_0https://id.loc.gov/authorities/subjects/sh85028802.
650 0 _aCombinatorial optimization.
_0https://id.loc.gov/authorities/subjects/sh85028809.
655 4 _aElectronic books.
856 4 0 _uhttps://onlinelibrary.wiley.com/doi/book/10.1002/9781394235971
_yFull text is available at Wiley Online Library Click here to view
942 _2ddc
_cER