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Computational Complexity of SAT XSAT and NAE-SAT ab 79.9 € als Taschenbuch: For linear and mixed Horn CNF formulas. Aus dem Bereich: Bücher, English, International, Gebundene Ausgaben,

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If you know how to program with Python and also know a little about probability, you’re ready to tackle Bayesian statistics. With this book, you'll learn how to solve statistical problems with Python code instead of mathematical notation, and use discrete probability distributions instead of continuous mathematics. Once you get the math out of the way, the Bayesian fundamentals will become clearer, and you’ll begin to apply these techniques to real-world problems. Bayesian statistical methods are becoming more common and more important, but not many resources are available to help beginners. Based on undergraduate classes taught by author Allen Downey, this book’s computational approach helps you get a solid start. * Use your existing programming skills to learn and understand Bayesian statistics * Work with problems involving estimation, prediction, decision analysis, evidence, and hypothesis testing * Get started with simple examples, using coins, M&Ms, Dungeons & Dragons dice, paintball, and hockey * Learn computational methods for solving real-world problems, such as interpreting SAT scores, simulating kidney tumors, and modeling the human microbiome.

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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 DesignJon Kleinberg and Eva TardosTable of Contents 1 Introduction: Some Representative Problems 1.1 A First Problem: Stable Matching 1.2 Five Representative Problems Solved ExercisesExcercisesNotes and Further Reading2 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 Reading3 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 Reading5 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 ExercisesExercisesNotes and Further Reading7 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 ExercisesExercisesNotes 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 Coloring8.8 Numerical Problems 8.9 Co-NP and the Asymmetry of NP8.10 A Partial Taxonomy of Hard Problems Solved Exercises Exercises Notes and Further Reading9 PSPACE: A Class of Problems Beyond NP9.1 PSPACE 9.2 Some Hard Problems in PSPACE 9.3 Solving Quantified Problems and Games in Polynomial Space9.4 Solving the Planning Problem in Polynomial Space9.5 Proving Problems PSPACE-Complete Solved ExercisesExercisesNotes and Further Reading 10 Extending the Limits of Tractability 10.1 Finding Small Vertex Covers 10.2 Solving NP-Hard Problem on Trees 10.3 Coloring a Set of Circular Arcs *10.4 Tree Decompositions of Graphs *10.5 Constructing a Tree Decomposition Solved Exercises Exercises Notes and Further Reading11 Approximation Algorithms 11.1 Greedy Algorithms and Bounds on the Optimum: A Load Balancing Problem 11.2 The Center Selection Problem 11.3 Set Cover: A General Greedy Heuristic 11.4 The Pricing Method: Vertex Cover 11.5 Maximization via the Pricing method: The Disjoint Paths Problem 11.6 Linear Programming and Rounding: An Application to Vertex Cover *11.7 Load Balancing Revisited: A More Advanced LP Application 11.8 Arbitrarily Good Approximations: the Knapsack Problem Solved ExercisesExercisesNotes and Further Reading 12 Randomized Algorithms 12.1 A First Application: Contention Resolution 12.2 Finding the Global Minimum Cut 12.3 Random Variables and their Expectations 12.4 A Randomized Approximation Algorithm for MAX 3-SAT 12.5 Randomized Divide-and-Conquer: Median-Finding and Quicksort 12.6 Hashing: A Randomized Implementation of Dictionaries 12.7 Finding the Closest Pair of Points: A Randomized Approach 12.8 Randomized Caching 12.9 Chernoff Bounds 12.10 Load Balancing *12.11 Packet Routing 12.12 Background: Some Basic Probability DefinitionsSolved ExercisesExercisesNotes and Further Reading 13 Local Search 13.1 The Landscape of an Optimization Problem 13.2 The Metropolis Algorithm and Simulated Annealing 13.3 An Application of Local Search to Hopfield Neural Networks 13.4 Maximum Cut Approximation via Local Search 13.5 Choosing a Neighbor Relation *13.6 Classification via Local Search 13.7 Best-Response Dynamics and Nash EquilibriaSolved ExercisesExercisesNotes aAugust 6, 2009 Author, Jon Kleinberg, was recently cited in the 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.

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Computational Complexity of SAT XSAT and NAE-SAT ab 79.9 EURO For linear and mixed Horn CNF formulas

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NP Complete (abbreviated as NPC) problems, standing at the crux of deciding whether P=NP, are among hardest problems in computer science and other related areas. Observing that NPC problems have different natures, they can be further classified. We show that the classification of NPC problems may depend on their natures, reduction methods, exact algorithms, and the boundary between P and NP. We propose a new perspective: both P problems and NPC problems have the duality feature in terms of computational complexity of asymptotic efficiency of algorithms. We then introduce near optimal solutions to some NPC problems such as Traveling Salesman Problems (TSP), Boolean Satisfiability Problems (SAT), Scheduling algorithms in Cloud data centers and Bigdata process platforms. These solutions may shine light on other NPC problems and their applications.

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The verification of systems to guarantee their correct behavior is discussed in this book. The mainly applied algorithmic method is the model checking technique combined with algorithms for solving the satisfiability problem (short: SAT). SAT-based verification of discrete systems has become one of the most effective technique within the last 10 years, such that industrial as well as academic applications heavily rely on it. The book covers the whole range of a SAT-based tool application. We propose extensions and concepts that concentrate on the core of a SAT-solver. However, these proposals are then transferred to novel verification models. Moreover, we describe approaches that incorporate the structure of the problem to exploit knowledge gained during the verification process on the level of the SAT-solver. The main focus of the book is on the verification of incomplete system designs, which occur for example in the early phase of a design. We describe various SAT-based modeling concepts that vary regarding their expressiveness and computational resources. The proposed methods are evaluated experimentally to guarantee their applicability in practice.

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The Boolean conjunctive normal form (CNF) satisability problem, called SAT for short, gets as input a CNF formula and has to decide whether this formula admits a satisfying truth assignment. As is well known, the remarkable result by S. Cook in 1971 established SAT as the first and genuine complete problem for the complexity class NP. In this thesis we consider SAT for a subclass of CNF, the so called Mixed Horn formula class (MHF). A formula F 2 MHF consists of a 2-CNF part P and a Horn part H. We propose that MHF has a central relevance in CNF because many prominent NP-complete problems, e.g. Feedback Vertex Set, Vertex Cover, Dominating Set and Hitting Set, can easily be encoded as MHF. Furthermore, we show that SAT remains NP-complete for some interesting subclasses of MHF. We also provide algorithms for some of these subclasses solving SAT in a better running time than O(2^0.5284n) which is the best bound for MHF so far. In addition, we investigate the computational complexity of some prominent variants of SAT, namely not-all-equal SAT (NAE-SAT) and exact SAT (XSAT) restricted to the class of linear CNF formulas.

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