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In 1958, Ralph E. Gomory transformed the field of integer programming when he published a paper that described a cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for integer programming. In 2008, to commemorate the anniversary of this seminal paper, a special workshop celebrating fifty years of integer programming was held in Aussois, France, as part of the 12th Combinatorial Optimization Workshop. It contains reprints of key historical articles and written versions of survey lectures on six of the hottest topics in the field by distinguished members of the integer programming community. Useful for anyone in mathematics, computer science and operations research, this book exposes mathematical optimization, specifically integer programming and combinatorial optimization, to a broad audience. In 1958, Ralph E. Gomory transformed the field of integer programming when he published a paper that described a cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for integer programming. In 2008, to commemorate the anniversary of this seminal paper, a special workshop celebrating fifty years of integer programming was held in Aussois, France, as part of the 12th Combinatorial Optimization Workshop. It contains reprints of key historical articles and written versions of survey lectures on six of the hottest topics in the field by distinguished members of the integer programming community. Useful for anyone in mathematics, computer science and operations research, this book exposes mathematical optimization, specifically integer programming and combinatorial optimization, to a broad audience. In 1958, Ralph E. Gomory transformed the field of integer programming when he published a short paper that described his cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for integer programming. In January of 2008, to commemorate the anniversary of Gomory´s seminal paper, a special session celebrating fifty years of integer programming was held in Aussois, France, as part of the 12th Combinatorial Optimization Workshop. This book is based on the material presented during this session. 50 Years of Integer Programming offers an account of featured talks at the 2008 Aussois workshop, namely - Michele Conforti, Gérard Cornuéjols, and Giacomo Zambelli: Polyhedral Approaches to Mixed Integer Linear Programming - William Cook: 50+ Years of Combinatorial Integer Programming - Francois Vanderbeck and Laurence A. Wolsey: Reformulation and Decomposition of Integer Programs The book contains reprints of key historical articles together with new introductions and historical perspectives by the authors: Egon Balas, Michel Balinski, Jack Edmonds, Ralph E. Gomory, Arthur M. Geoffrion, Alan J. Hoffman & Joseph B. Kruskal, Richard M. Karp, Harold W. Kuhn, and Ailsa H. Land & Alison G. Doig. It also contains written versions of survey lectures on six of the hottest topics in the field by distinguished members of the integer programming community: - Friedrich Eisenbrand: Integer Programming and Algorithmic Geometry of Numbers - Raymond Hemmecke, Matthias Köppe, Jon Lee, and Robert Weismantel: Nonlinear Integer Programming - Andrea Lodi: Mixed Integer Programming Computation - Francois Margot: Symmetry in Integer Linear Programming - Franz Rendl: Semidefinite Relaxations for Integer Programming - Jean-Philippe P. Richard and Santanu S. Dey: The Group-Theoretic Approach to Mixed Integer Programming Integer programming holds great promise for the future, and continues to build on its foundations. Indeed, Gomory´s finite cutting-plane method for the pure integer case is currently being reexamined and is showing new promise as a practical computational method. This book is a uniquely useful celebration of the past, present and future of this important and active field. Ideal for students and researchers in mathematics, computer science and operations research, it exposes mathematical optimization, in particular integer programming and combinatorial optimization, to a broad audience.

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Studienarbeit aus dem Jahr 2003 im Fachbereich Informatik - Wirtschaftsinformatik, Note: gut, Universität zu Köln (Seminar für WI und OR), Veranstaltung: Hauptseminar zum Operations Research, 18 Quellen im Literaturverzeichnis, Sprache: Deutsch, Abstract: Ziel des Revenue Managements ist es, durch den Einsatz von Methoden des Operations Research zusätzliche Erlöspotentiale, die sich insbesondere aus unterschiedlichen Preisbereitschaften der Kunden ergeben, möglichst weitgehend auszunutzen. Die Grundidee des Revenue Management ist dabei die folgende: man möchte heute etwas nicht zu einem niedrigen Preis verkaufen, wenn man es später zu einem höheren Preis verkaufen kann; gleichzeitig will man das Gut jedoch heute zu einem niedrigen Preis verkaufen, falls es andernfalls später überhaupt nicht verkauft werden kann. Damit möchte man die Erlöse aus dem Verkauf einer feststehenden Menge eines Gutes maximieren, indem man dem Kunden das Gut zu dem höchstmöglichsten Preis, den er bereit ist zu zahlen, anbietet. Die vorliegende Arbeit ist wie folgt aufgebaut: Zuerst erfolgt in Kapitel 2 eine allgemeine Einführung in das Revenue Management. Dabei werden die Komponenten des Revenue Management (Datenbeschaffung und Forecasting, Preissteuerung, Kapazitätssteuerung, und Ergebniskontrolle) allgemein erläutert und ihr Zusammenhang dargestellt. In Kapitel 3 wird dann konkret auf das älteste und am meisten verbreitete Einsatzgebiet eingegangen, das Airline Revenue Management. Dabei werden zuerst die besonderen Charakteristika des Airline Revenue Management hervorgehoben, und anschließend auf die wichtigsten Komponenten (Overbooking, Pricing und Seat Inventory Control) eingegangen. Der Schwerpunkt liegt dabei auf dem Seat Inventory Control, da hierbei die Methoden des Operations Research am Wichtigsten sind. Es werden allgemeine Modelle für das Network Revenue Management vorgestellt, bei denen vom allgemeinen stochastischen Modell auf das Integer Programming Modell und schließlich auf das Linear Programming Modell geschlossen wird. Außerdem werden 2 konkrete Methoden zur Implementierung vorgestellt, nämlich Nesting der Buchungsklassen und Bid-Preise. In Kapitel 4 schließlich wird ein Ausblick auf zukünftige Forschungsrichtungen gewährt und es werden kurz einige Inhalte erläutert, die aus Platzgründen keinen Platz in dieser Arbeit finden konnten.

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There are many surprising connections between the theory of numbers, which is one of the oldest branches of mathematics, and computing and information theory. Number theory has important applications in computer organization and security, coding and cryptography, random number generation, hash functions, and graphics. Conversely, number theorists use computers in factoring large integers, determining primes, testing conjectures, and solving other problems. This book takes the reader from elementary number theory, via algorithmic number theory, to applied number theory in computer science. It introduces basic concepts, results, and methods, and discusses their applications in the design of hardware and software, cryptography, and security. It is aimed at undergraduates in computing and information technology, but will also be valuable to mathematics students interested in applications. In this 2nd edition full proofs of many theorems are added and some corrections are made.

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This book is an essential desktop reference for the CERT C coding standard. The CERT C Coding Standard is an indispensable collection of expert information. The standard itemizes those coding errors that are the root causes of software vulnerabilities in C and prioritizes them by severity, likelihood of exploitation, and remediation costs. Each guideline provides examples of insecure code as well as secure, alternative implementations. If uniformly applied, these guidelines will eliminate the critical coding errors that lead to buffer overflows, format string vulnerabilities, integer overflow, and other common software vulnerabilities.

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This highly comprehensive handbook provides a substantial advance in the computation of elementary and special functions of mathematics, extending the function coverage of major programming languages well beyond their international standards, including full support for decimal floating-point arithmetic. Written with clarity and focusing on the C language, the work pays extensive attention to little-understood aspects of floating-point and integer arithmetic, and to software portability, as well as to important historical architectures. It extends support to a future 256-bit, floating-point format offering 70 decimal digits of precision. Select Topics and Features: references an exceptionally useful, author-maintained MathCW website, containing source code for the book´s software, compiled libraries for numerous systems, pre-built C compilers, and other related materials; offers a unique approach to covering mathematical-function computation using decimal arithmetic; provides extremely versatile appendices for interfaces to numerous other languages: Ada, C#, C++, Fortran, Java, and Pascal; presupposes only basic familiarity with computer programming in a common language, as well as early level algebra; supplies a library that readily adapts for existing scripting languages, with minimal effort; supports both binary and decimal arithmetic, in up to 10 different floating-point formats; covers a significant portion (with highly accurate implementations) of the U.S National Institute of Standards and Technology´s 10-year project to codify mathematical functions. This highly practical text/reference is an invaluable tool for advanced undergraduates, recording many lessons of the intermingled history of computer hardw are and software, numerical algorithms, and mathematics. In addition, professional numerical analysts and others will find the handbook of real interest and utility because it builds on research by the mathematical software community over the last four decades.

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In Hacker?s Delight, Second Edition , Hank Warren once again compiles an irresistible collection of programming hacks: timesaving techniques, algorithms, and tricks that help programmers build more elegant and efficient software, while also gaining deeper insights into their craft. Warren?s hacks are eminently practical, but they?re also intrinsically interesting, and sometimes unexpected, much like the solution to a great puzzle. They are, in a word, a delight to any programmer who is excited by the opportunity to improve. Extensive additions in this edition include A new chapter on cyclic redundancy checking (CRC), including routines for the commonly used CRC-32 code A new chapter on error correcting codes (ECC), including routines for the Hamming code More coverage of integer division by constants, including methods using only shifts and adds Computing remainders without computing a quotient More coverage of population count and counting leading zeros Array population count New algorithms for compress and expand An LRU algorithm Floating-point to/from integer conversions Approximate floating-point reciprocal square root routine A gallery of graphs of discrete functions Now with exercises and answers Product Description In Hacker?s Delight, Second Edition , Hank Warren once again compiles an irresistible collection of programming hacks: timesaving techniques, algorithms, and tricks that help programmers build more elegant and efficient software, while also gaining deeper insights into their craft. Warren?s hacks are eminently practical, but they?re also intrinsically interesting, and sometimes unexpected, much like the solution to a great puzzle. They are, in a word, a delight to any programmer who is excited by the opportunity to improve. Extensive additions in this edition include A new chapter on cyclic redundancy checking (CRC), including routines for the commonly used CRC-32 code A new chapter on error correcting codes (ECC), including routines for the Hamming code More coverage of integer division by constants, including methods using only shifts and adds Computing remainders without computing a quotient More coverage of population count and counting leading zeros Array population count New algorithms for compress and expand An LRU algorithm Floating-point to/from integer conversions Approximate floating-point reciprocal square root routine A gallery of graphs of discrete functions Now with exercises and answers Foreword xiii Preface xv Chapter 1: Introduction 1 1.1 Notation 1 1.2 Instruction Set and Execution Time Model 5 Chapter 2: Basics 11 2.1 Manipulating Rightmost Bits 11 2.2 Addition Combined with Logical Operations 16 2.3 Inequalities among Logical and Arithmetic Expressions 17 2.4 Absolute Value Function 18 2.5 Average of Two Integers 19 2.6 Sign Extension 19 2.7 Shift Right Signed from Unsigned 20 2.8 Sign Function 20 2.9 Three-Valued Compare Function 21 2.10 Transfer of Sign Function 22 2.11 Decoding a ?Zero Means 2** n ? Field 22 2.12 Comparison Predicates 23 2.13 Overflow Detection 28 2.14 Condition Code Result of Add , Subtract , and Multiply 36 2.15 Rotate Shifts 37 2.16 Double-Length Add/Subtract 38 2.17 Double-Length Shifts 39 2.18 Multibyte Add , Subtract , Absolute Value 40 2.19 Doz, Max, Min 41 2.20 Exchanging Registers 45 2.21 Alternating among Two or More Values 48 2.22 A Boolean Decomposition Formula 51 2.23 Implementing Instructions for all 16 Binary Boolean Operations 53 Chapter 3: Power-of-2 Boundaries 59 3.1 Rounding Up/Down to a Multiple of a Known Power of 2 59 3.2 Rounding Up/Down to the Next Power of 2 60 3.3 Detecting a Power-of-2 Boundary Crossing 63 Chapter 4: Arithmetic Bounds 67 4.1 Checking Bounds of Integers 67 4.2 Propagating Bounds through Add ?s and Subtract ?s 70 4.3 Propagating Bounds through Logical Operations 73 Chapter 5: Counting Bits 81 5.1 Counting 1-Bits 81 5.2 Parity 96 5.3 Counting Leading 0?s 99 5.4 Counting Trailing 0?s 107 Chapter 6: Searching Words 117 6.1 Find First 0-Byte 117 6.2 Find First String of 1-Bits of a Given Length 123 6.3 Find Longest String of 1-Bits 125 6.4 Find Shortest String of 1-Bits 126 Chapter 7: Rearranging Bits And Bytes 129 7.1 Reversing Bits and Bytes 129 7.2 Shuffling Bits 139 7.3 Transposing a Bit Matrix 141 7.4 Compress , or Generalized Extract 150 7.5 Expand , or Generalized Insert 156 7.6 Hardware Algorithms for Compress and Expand 157 7.7 General Permutations, Sheep and Goats Operation 161 7.8 Rearrangements and Index

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For courses in Computer Science and Programming Computer systems: A Programmer?s Perspective explains the underlying elements common among all computer systems and how they affect general application performance. Written from the programmer?s perspective, this book strives to teach students how understanding basic elements of computer systems and executing real practice can lead them to create better programs. Spanning across computer science themes such as hardware architecture, the operating system, and systems software, the Third Edition serves as a comprehensive introduction to programming. This book strives to create programmers who understand all elements of computer systems and will be able to engage in any application of the field--from fixing faulty software, to writing more capable programs, to avoiding common flaws. It lays the groundwork for students to delve into more intensive topics such as computer architecture, embedded systems, and cybersecurity. This book focuses on systems that execute an x86-64 machine code, and recommends that students have access to a Linux system for this course. Students should have basic familiarity with C or C++. MasteringEngineering ® not included. Students, if MasteringEngineering is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN and course ID. MasteringEngineering should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information. MasteringEngineering is an online homework, tutorial, and assessment product designed to personalize learning and improve results. With a wide range of interactive, engaging, and assignable activities, students are encouraged to actively learn and retain tough course concepts. Features + Benefits This title is a Pearson Global Edition. The Editorial team at Pearson has worked closely with educators around the world to include content which is especially relevant to students outside the United States. Computer Systems: A Programmer?s Perspective uses the following features to facilitate learning: NEW! The book now exclusively bases its presentation on x86-64 A carefully planned 12 chapter layout that covers all of the core topics of computer programming Chapter 1 uses a simple ?hello world? program to introduce the major concepts and themes of computer programming. Chapter 2 dives into the topic of computer arithmetic, considering how numbers are represented in computer programs and how they affect value coding. The chapter places a special emphasis on the properties of unsigned and two?s-compliment number representations. It gives students necessary insight into arithmetic from the programmers perspective and why it?s so important. Chapter 3 teaches students how to read the x86-64 code generated by a C compiler, covering the basic instruction patterns for different control constructs, implementation procedures, and the allocation of different data structures. This chapter also discusses the implementation of integer and floating point arithmetic and takes a machine-level view of programs to understand certain code vulnerabilities. Chapter 4 introduces students to basic combinational and sequential logic elements and shows how they can be used in a simplified subset of the x86-64 instruction set called Y86-64. It starts with a single-cycle datapath and moves onto a discussion of pipelining. Chapter 5 gives students techniques for improving code performance with transformations that reduce work and enhance instruction-level parallelism. Chapter 6 covers different types of RAM and ROM memory systems, describing their hierarchical arrangement. The chapter makes the abstract concept tangible by using the analogy of a ?memory mountain? with ridges of temporal locality and slopes of spatial locality. Students learn that improving temporal and spatial locality improves performance. Chapter 7 discusses both static and dynamic linking, areas included in most systems text where programmers make their most confusing errors. Chapter 8 explains exceptional control flow at all levels of the system, from simple hardware interrupts to nonlocal jumps in C that break the stack discipline. This chapter introduces the fundamental idea of a process by teaching students how it works and how it is created and manipulated from application programs. Chapter 9 shows students key characteristics of the virtual memory system and how it works, addressing issues such

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August 6, 2009 Author, Jon Kleinberg, was recently cited in the New York Times for his statistical analysis research in the Internet age. Algorithm Design introduces algorithms by looking at the real-world problems that motivate them. The book teaches students a range of design and analysis techniques for problems that arise in computing applications. The text encourages an understanding of the algorithm design process and an appreciation of the role of algorithms in the broader field of computer science. Features + Benefits Focus on problem analysis and design techniques. Discussion is grounded in concrete problems and examples rather than abstract presentation of principles, with representative problems woven throughout the text. Over 200 well crafted problems from companies such as Yahoo!® and Oracle®. Each problem has been class tested for usefulness and accuracy in the authors´ own undergraduate algorithms courses. Broad coverage of algorithms for dealing with NP-hard problems and the application of randomization, increasingly important topics in algorithms. Algorithm Design Jon Kleinberg and Eva Tardos Table of Contents 1 Introduction: Some Representative Problems 1.1 A First Problem: Stable Matching 1.2 Five Representative Problems Solved Exercises Excercises Notes and Further Reading 2 Basics of Algorithms Analysis 2.1 Computational Tractability 2.2 Asymptotic Order of Growth Notation 2.3 Implementing the Stable Matching Algorithm using Lists and Arrays 2.4 A Survey of Common Running Times 2.5 A More Complex Data Structure: Priority Queues Solved Exercises Exercises Notes and Further Reading 3 Graphs 3.1 Basic Definitions and Applications 3.2 Graph Connectivity and Graph Traversal 3.3 Implementing Graph Traversal using Queues and Stacks 3.4 Testing Bipartiteness: An Application of Breadth-First Search 3.5 Connectivity in Directed Graphs 3.6 Directed Acyclic Graphs and Topological Ordering Solved Exercises Exercises Notes and Further Reading 4 Divide and Conquer 4.1 A First Recurrence: The Mergesort Algorithm 4.2 Further Recurrence Relations 4.3 Counting Inversions 4.4 Finding the Closest Pair of Points 4.5 Integer Multiplication 4.6 Convolutions and The Fast Fourier Transform Solved Exercises Exercises Notes and Further Reading 5 Greedy Algorithms 5.1 Interval Scheduling: The Greedy Algorithm Stays Ahead 5.2 Scheduling to Minimize Lateness: An Exchange Argument 5.3 Optimal Caching: A More Complex Exchange Argument 5.4 Shortest Paths in a Graph 5.5 The Minimum Spanning Tree Problem 5.6 Implementing Kruskal´s Algorithm: The Union-Find Data Structure 5.7 Clustering 5.8 Huffman Codes and the Problem of Data Compression *5.9 Minimum-Cost Arborescences: A Multi-Phase Greedy Algorithm Solved Exercises Excercises Notes and Further Reading 6 Dynamic Programming 6.1 Weighted Interval Scheduling: A Recursive Procedure 6.2 Weighted Interval Scheduling: Iterating over Sub-Problems 6.3 Segmented Least Squares: Multi-way Choices 6.4 Subset Sums and Knapsacks: Adding a Variable 6.5 RNA Secondary Structure: Dynamic Programming Over Intervals 6.6 Sequence Alignment 6.7 Sequence Alignment in Linear Space 6.8 Shortest Paths in a Graph 6.9 Shortest Paths and Distance Vector Protocols *6.10 Negative Cycles in a Graph Solved Exercises Exercises Notes and Further Reading 7 Network Flow 7.1 The Maximum Flow Problem and the Ford-Fulkerson Algorithm 7.2 Maximum Flows and Minimum Cuts in a Network 7.3 Choosing Good Augmenting Paths *7.4 The Preflow-Push Maximum Flow Algorithm 7.5 A First Application: The Bipartite Matching Problem 7.6 Disjoint Paths in Directed and Undirected Graphs 7.7 Extensions to the Maximum Flow Problem 7.8 Survey Design 7.9 Airline Scheduling 7.10 Image Segmentation 7.11 Project Selection 7.12 Baseball Elimination *7.13 A Further Direction: Adding Costs to the Matching Problem Solved Exercises Exercises Notes and Further Reading 8 NP and Computational Intractability 8.1 Polynomial-Time Reductions 8.2 Reductions via ´´Gadgets´´: The Satisfiability Problem 8.3 Efficient Certification and the Definition of NP 8.4 NP-Complete Problems 8.5 Sequencing Problems 8.6 Partitioning Problems 8.7 Graph Coloring 8.8 Numerical Problems 8.9 Co-NP and the Asymmetry of NP 8.10 A Partial Taxonomy of Hard Problems Solved Exercises Exercises Notes and Further Reading 9 PSPACE: A Class of Problems Beyond NP 9.1 PSPACE 9.2 Some Hard Problems in PSPACE 9.3 Solving Quantified Problems and Games in Polynomial Space 9.4 Solving the Planning

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