Explaining how to apply to mathematical programming to network design and control, Linear Programming and Algorithms for Communication Networks: A Practical Guide to Network Design, Control, and Management fills the gap between mathematical programming theory and its implementation in communication networks. From the basics all the way through to more advanced concepts, its comprehensive coverage provides readers with a solid foundation in mathematical programming for communication networks.
Addressing optimization problems for communication networks, including the shortest path problem, max flow problem, and minimum-cost flow problem, the book covers the fundamentals of linear programming and integer linear programming required to address a wide range of problems. It also:
Using the GNU Linear Programming Kit (GLPK) package, which is designed for solving linear programming and mixed integer programming problems, it explains typical problems and provides solutions for communication networks. The book provides algorithms for these problems as well as helpful examples with demonstrations. Once you gain an understanding of how to solve LP problems for communication networks using the GLPK descriptions in this book, you will also be able to easily apply your knowledge to other solvers.
Understanding programming and programming languages requires knowledge of the underlying theoretical model. This book explores aspects of programming that are amenable to mathematical proof. The author describes a programming theory which is much simpler and more comprehensive than the current theories to date. In the theoretical model, a specification is just a boolean expression and refinement is just an ordinary implication. The author develops a practical and broad method for writing precise specifications and designing programs whose executions probably satisfy the specifications. Beginning with preparatory material in logic, numbers, sets, lists, functions and relations, the book advances further into program theory, the heart of the book. Subsequent chapters may be selected or omitted according to course emphasis. The text will be useful to students in courses on programming methodology or verification at the advanced undergraduate or beginning graduate level, as well as for software engineers in the field. All technical terms are explained and then demonstrated in the book wherever possible. No advanced mathematical knowledge or programming language is assumed. The book contains numerous exercises and worked-out solutions for specific exercises. Transparency masters and solutions for the remaining exercises are available from the author.
Foundation of logic historically dates back to the times of Aristotle, who pioneered the concept of truth/falsehood paradigm in reasoning. Mathematical logic of propositions and predicates, which are based on the classical models of Aristotle, underwent a dramatic evolution during the last 50 years for its increasing applications in automated reasoning on digital computers. The subject of Logic Programming is concerned with automated reasoning with facts and knowledge to answer a user s query following the syntax and semantics of the logic of propositions/predicates. The credit of automated reasoning by logic programs goes to Professor Robinson for his well-known resolution theorem that provides a general scheme to select two program clauses for deriving an inference. Until now Robinson s theorem is being used in PROLOG/DATALOG compilers to automatically build a Select Linear Definite (SLD) clause based resolution tree for answering a user s query. The SLD-tree based scheme for reasoning undoubtedly opened a new era in logic programming for its simplicity in implementation in the compilers. In fact, SLD-tree construction suffices the need for users with a limited set of program clauses. But with increase in the number of program clauses, the execution time of the program also increases linearly by the SLD-tree based approach. An inspection of a large number of logic programs, however, reveals that more than one pair of program clauses can be resolved simultaneously without violating the syntax and the semantics of logic programming. This book employs this principle to speed up the execution time of logic programs."
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