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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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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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This book studies two optimization problems, maximum satisfiability and planing of satisfiability. The maximum satisfiability problem (max-SAT) is the optimization counterpart of the satisfiability problem (SAT). The goal of max-SAT is to maximize the number of clauses satisfied. planning as satisfiability is a class of planning aiming to achieve a plan with optimal resource, cost, or makespan by using the SAT approach. We present a mix- SAT formulation for these two optimization problems and examine to extend the Davis-Putnam-Logemann- Loveland (DPLL) procedure, which is the basic framework for the original SAT problem, for this mix- SAT formulation. We progressively develop a series of algorithms and reconsider many general SAT techniques for these two optimization problems.

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Drawing graphs is a discipline in graph theory,dealing with the optimal representation of graphs. Animportant class of graphs are the planar graphs,which can be drawn without any intersecting edges.Such graphs are superior in terms of humanreadability. Radial level graphs are a specific classof graphs that only have edges between vertices ofdifferent levels, which are arranged in concentriccircles. The knowledge about the planarity of a graphenables the use of more efficient algorithms todisplay good representations. In this book, severalapproaches are discussed to describe the problem ofradial level planarity in a propositional logicframework. A model is introduced that describes theproblem as a SAT problem and for some types of graphseven as a 2-SAT problem, which is solvable in lineartime. The truth assignment of the variables describesthe non-intersecting embedding. Additionally, themodel is capable of introducing vertices-grouping,enabling the modelling of semantic rules. This bookis aiming for scientists that do research in thefields of graph drawing and/or propositional networksand theoretical informatics as well as for interestedstudents.

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Revision with unchanged content. Automatic program analysis tools are increasingly developed and deployed to combat the perenniel software quaility problem that plagues the IT industry. Traditional tools faces a stark tradeoff between precision and scalability: scalable tools are often imprecise, limiting themselves to detecting relatively shallow errors, precise tools are often not scalable and are thus only applied to simplified models of the core parts of large systems. This study presents techniques and results on how to exploit existing struc tures of large software systems to make precise program analyses scale. As an example, the author show how to scale Boolean Satisfiability (SAT) based a na lysis - traditionally applied to small models with hundreds of lines of code - to the whole Linux kernel, which contains millions of lines of code. This study is directed to designers and users of software analysis tools alike. It offers detailed descriptions of several state-of-the-art automatic error detection algorithms and presents experimental results on mature open-source systems. The approach can be potentially generalized to the design and deployment of a wide range of program analysis tools.

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Membrane Computing (P Systems) is an emergent and promising branch of Natural Computing. Designing P Systems is a heavy difficult problem. Until now there is no tool exists that can help in designing of P systems. This book shows how to use clonal selection algorithm with adaptive mutation in the design of P systems. In Addition the book proposes a Membrane-Immune algorithm that is inspired from the structure of living cells and the vertebrate immune system. The algorithm is tested by solving the Multiple Zero/One Knapsack Problem. The Membrane-Immune algorithm surpassed two variants of genetic algorithms that solved the same problem. The Membrane-Immune algorithm is also applied to generate a fuzzy rule based system to be used in breast cancer diagnosis. Generating a fuzzy rule system composes an exponential search space, which leads to the area of NP-complete problems. The algorithm is compared with five techniques and surpassed them. Last chapter presents a proposal of P Systems implementation using Cloud Computing. The proposed Implementation is illustrated by solving SAT problem.

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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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