The famous simplex method, invented by George B. Dantzig in 1947, moves from vertex to vertex in the underlying polyhedron until achieving an optimal vertex. As one of the most widely used mathematical tools, it has dominated the field of Linear Programming for nearly eighty years. However, it has exponential time complexity, and its performance turned out somehow unsatisfactory when solving some difficult LP problems since the solution process can sink into a degenerate vertex for too lon...

This monograph represents a historic breakthrough in the field of linear programming (LP)since George Dantzig first discovered the simplex method in 1947.Being both thoughtful and informative, it focuses on reflecting and promoting the state of the art by highlighting new achievements in LP. This new edition is organized in two volumes. The first volume addresses foundations of LP, including the geometry of feasible region, the simplex method and its implementation, duality and the...

With emphasis on computation, this book is a real breakthrough in the field of LP. In addition to conventional topics, such as the simplex method, duality, and interior-point methods, all deduced in a fresh and clear manner, it introduces the state of the art by highlighting brand-new and advanced results, including efficient pivot rules, Phase-I approaches, reduced simplex methods, deficient-basis methods, face methods, and pivotal interior-point methods. In particular, it covers the dete...

A comprehensive update of the leading algorithms text, with new material on matchings in bipartite graphs, online algorithms, machine learning, and other topics.Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. It covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers, wi...

&>The bible of all fundamental algorithms and the work that taught many of today's software developers most of what they know about computer programming.—Byte, September 1995I can't begin to tell you how many pleasurable hours of study and recreation they have afforded me! I have pored over them in cars, restaurants, at work, at home... and even at a Little League game when my son wasn't in the line-up.—Charles LongIf you think you're a...

The bible of all fundamental algorithms and the work that taught many of today's software developers most of what they know about computer programming.–Byte, September 1995I can't begin to tell you how many pleasurable hours of study and recreation they have afforded me! I have pored over them in cars, restaurants, at work, at home... and even at a Little League game when my son wasn't in the line-up.–Charles LongIf you think y...

Optimization is an essential technique for solving problems in areas as diverse as accounting, computer science and engineering. Assuming only basic linear algebra and with a clear focus on the fundamental concepts, this textbook is the perfect starting point for first- and second-year undergraduate students from a wide range of backgrounds and with varying levels of ability. Modern, real-world examples motivate the theory throughout. The authors keep the text as concise and focused as pos...

This textbook provides an engaging and motivational introduction to traditional topics in discrete mathematics, in a manner specifically designed to appeal to computer science students. The text empowers students to think critically, to be effective problem solvers, to integrate theory and practice, and to recognize the importance of abstraction.Clearly structured and interactive in nature, the book presents detailed walkthroughs of several algorithms, stimulating a conversation wi...

This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set. The book starts with a bro...

Problem solving is an essential part of every scientific discipline. It has two components: (1) problem identification and formulation, and (2) the solution to the formulated problem. One can solve a problem on its own using ad hoc techniques or by following techniques that have produced efficient solutions to similar problems. This requires the understanding of various algorithm design techniques, how and when to use them to formulate solutions, and the context appropriate for each of the...

The focus of this book is the P versus NP Question and the theory of NP-completeness. It also provides adequate preliminaries regarding computational problems and computational models. The P versus NP Question asks whether or not finding solutions is harder than checking the correctness of solutions. An alternative formulation asks whether or not discovering proofs is harder than verifying their correctness. It is widely believed that the answer to these equivalent formulations is positive...

Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians.The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definit...