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.
Subgroup theorems and graphs.- Counting unlabeled acyclic digraphs.- Golay sequences.- The knotted hexagon.- On skew room squares.- Some new constructions for orthogonal designs using circulants.- A note on asymptotic existence results for orthogonal designs.- The spectrum of a graph.- Latin squares composed of four disjoint subsquares.- The semi-stability of lexicographic products.- On rings of circuits in planar graphs.- Sum-free sets in loops.- Groups with stable graphs.- A problem in the design of electrical circuits, a generalized subadditive inequality and the recurrence relation j(n,m)=j([n/2],m)+j([n+1/2],m)+j(n,m¿1).- Orthogonal designs in order 24.- A schr¿der triangle: Three combinatorial problems.- A combinatorial approach to map theory.- On quasi-multiple designs.- A generalisation of the binomial coefficients.
This monograph (in two volumes) deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs, and in physics, as stable equilibrium configuations in nonlinear elasticity or for liquid crystals. The presentation is selfcontained and accessible to non specialists. Topics are treated as far as possible in an elementary way, illustrating results with simple examples; in principle, chapters and even sections are readable independently of the general context, so that parts can be easily used for graduate courses. Open questions are often mentioned and the final section of each chapter discusses references to the literature and sometimes supplementary results. Finally, a detailed 'Table of contents' and an extensive 'Index' are of help to consult this monograph.
On the assumptions of a central limit theorem for approximate martingale arrays on a group.- Idempotent measures on commutative hypergroups.- Les variables aleatoires de loi stable et leur representation selon P. Levy.- Parabolic subgroups and factor compactness of measures on semisimple lie groups.- Une caracterisation du type de la loi de Cauchy-Heisenberg.- Levy-Schoenberg kernels on riemannian symmetric spaces of noncompact type.- Exemples d'hypergroupes transients.- Quelques proprietes du noyau potentiel d'une marche aleatoire sur les hypergroupes de type Kunze-Stein.- Sobolev inequalities and random walks.- Uniform distribution in solvable groups.- Absolute continuity and singularity of distributions of dependent observations: Gaussian and exchangeable measures.- Ergodic and mixing properties of measures on locally compact groups.- On jumps of paths of Markov processes.- Recurrent random walks on homogeneous spaces.- A central limit theorem for coalgebras.- Haar measures in a representation and a decomposition problem.- Compactness, medians and moments.- Non-commutative algebraic central limit theorems.- A description of the martin boundary for nearest neighbour random walks on free products.- On hyperbolic hypergroups.- Theoremes de la limite centrale pour les produits de matrices en dependance Markovienne. Resultats recents.- Entropie, theoremes limite et marches aleatoires.- Random walks on graphs.- Stable probability measures on groups and on vector spaces.- Towards a duality theory for algebras.- Random fields on noncommutative locally compact groups.
Learn all about technical analysis and chart a course for a stable financial future Interested in incorporating technical analysis into your investment strategy but feeling a bit at sea when it comes to making sense of all the charts and tools? Here's your lifeline! With help from Technical Analysis Demystified, you'll have big profits in your forecast. Chartered Market Technician Constance Brown explains the many different types of technical analysis tools and how to use them. Key topics covered include charting, moving averages, trends and cycles, oscillators, market patterns, Fibonacci ratios, price data, risk-to-reward ratios, and much more. Featuring end-of-chapter quizzes and a glossary, this straightforward guide makes technical analysis easy to understand and apply to your strategy of spotting-and profiting from-market trends and patterns. This fast and easy guide offers: Clear explanations of charting techniques Time-tested trading rules and guidelines Valuable charts, graphs, and figures Strategies for developing your own system for analyzing the market Detailed descriptions of real-time trades Simple enough for a novice but in-depth enough for a seasoned investor, Technical Analysis Demystified will help you capitalize on market cycles.
With numerous charts, graphs, and a glossary of change--management terms, this book is both an ideal blueprint and an accessible quick reference for the implementation of stable and sustained transformation.
Some properties of H-designs.- Computation of some number-theoretic coverings.- The search for long paths and cycles in vertex-transitive graphs and digraphs.- On strongly hamiltonian abelian group graphs.- Monochromatic lines in partitions of Zn.- Complete stable marriages and systems of I-M preferences.- The construction of finite projective planes.- A survey of graph generation techniques.- Graphs and two-distance sets.- Finite Ramsey theory is hard.- Further results on coverin integers of the form 1+k2N by primes.- Distributive block structures and their automorphisms.- Connected subgraphs of the graph of multigraphic realisations of a degree sequence.- A construction for a family of sets and its application to matroids.- Regularity and optimality for trees.- Simple and multigraphic realizations of degree sequences.- Critical link identification in a network.- Enumeration of binary phylogenetic trees.- Minimisatin of multiple entry finite automata.- A singular direct product for quadruple systems.- The maximum number of intercalates in a latin square.- Elegant odd rings and non-planar graphs.- On critical sets of edges in graphs.- Further evidence for a conjecture on two-point deleted subgraphs of cartesian products.- Deques, trees and lattice paths.- Graeco-latin and nested row and column designs.- Contrained switchings in graphs.- One-factorisations of wreath products.- Divisible semisymmetric designs.- Graphs and universal algebras.- Universal fabrics.
This introduction to random walks on infinite graphs gives particular emphasis to graphs with polynomial volume growth. It offers an overview of analytic methods, starting with the connection between random walks and electrical resistance, and then proceeding to study the use of isoperimetric and Poincare inequalities. The book presents rough isometries and looks at the properties of a graph that are stable under these transformations. Applications include the 'type problem': determining whether a graph is transient or recurrent. The final chapters show how geometric properties of the graph can be used to establish heat kernel bounds, that is, bounds on the transition probabilities of the random walk, and it is proved that Gaussian bounds hold for graphs that are roughly isometric to Euclidean space. Aimed at graduate students in mathematics, the book is also useful for researchers as a reference for results that are hard to find elsewhere.
This volume contains contributions to the Séminaire de Mathématiques Supérieures - NATO Advanced Study Institute on ``Morse theoretic Methods in non-linear Analysis and Symplectic Topology' which was held at the Université de Montréal in the summer of 2004. The recent years have witnessed the emergence of a deeper and more general formalism of the main geometric ideas in these fields. The surveys and research papers in this volume are a striking example of this trend. They provide an up-to-date overview of some of the most significant advances in these topics. The text is of high relevance for graduate students as well as for more senior mathematicians with interest in a wide range of topics going from symplectic topology to dynamical systems and from algebraic and differential topology to variational methods. TOC:Preface.Contributors. Lectures on the Morse Complex for Infinite-Dimensional Manifolds.-1. A few facts from hyperbolic dynamics.-1.1 Adapted norms .-1.2 Linear stable and unstable spaces of an asymptotically hyperbolic path.-1.3 Morse vector fields.- 1.4 Local dynamics near a hyperbolic rest point ; 1.5 Local stable and unstable manifolds.- 1.6 The Grobman - Hartman linearization theorem.-1.7 Global stable and unstable manifolds.- 2 The Morse complex in the case of finite Morse indices.- 2.1 The Palais - Smale condition.-2.2 The Morse - Smale condition .-2.3 The assumptions .- 2.4 Forward compactness.- 2.5 Consequences of compactness and transversality.- 2.6 Cellular filtrations.- 2.7 The Morse complex.- 2.8 Representation of $delta$* in terms of intersection numbers.- 2.9 How to remove the assumption (A8).- 2.10 Morse functions on Hilbert manifolds.-2.11 Basic results in transversality theory .- 2.12 Genericity of the Morse - Smale condition.-2.13 Invariance of the Morse complex.- 3 The Morse complex in the case of infinite Morse indices.- 3.1 The program.-3.2 Fredholm pairs and compact perturbations of linear subspaces.- 3.3 Finite-dimensional intersections.-3.4 Essential subbundles.- 3.5 Orientations.- 3.6 Compactness .- 3.7 Two-dimensional intersections .-3.8 The Morse complex.- Bibliographical note.- Notes on Floer Homology and Loop Space Homology.- 1 Introduction.- 2 Main result.-2.1 Loop space homology.-2.2 Floer homology for the cotangent bundle.- 3 Ring structures and ring-homomorphisms.-3.1 The pair-of-pants product.- 3.2 The ring homomorphisms between free loop space Floer homology and based loop space Floer homology and classical homology.-4 Morse-homology on the loop spaces $Lambda$Q and $Omega$Q, and the isomorphism.-5 Products in Morse-homology .-5.1 Ring isomorphism between Morse homology and Floer homology.- Homotopical Dynamics in Symplectic Topology.- 1 Introduction .-2 Elements of Morse theory .-2.1 Connecting manifolds.-2.2 Operations.-3 Applications to symplectic topology.- 3.1 Bounded orbits .-3.2 Detection of pseudoholomorphic strips and Hofer's norm.- Morse Theory, Graphs, and String Topology.-1 Graphs, Morse theory, and cohomology operations.-2 String topology .-3 A Morse theoretic view of string topology.- 4 Cylindrical holomorphic curves in the cotangent bundle.- Topology of Robot Motion Planning.-1.Introduction .-2 First examples of configuration spaces .-3 Varieties of polygonal linkages.-3.1 Short and long subsets .-3.2 Poincaré polynomial of M(a) .-4 Universality theorems for configuration spaces .-5 A remark about configuration spaces in robotics .-6 The motion planning problem.-7 Tame motion planning algorithms.-8 The Schwarz genus.- 9 The second notion of topological complexity.-10 Homotopy invariance.- 11 Order of instability of a motion planning algorithm.-12 Random motion planning algorithms.- 13 Equality theorem.-14 An upper bound for TC(X).-15 A cohomological lower bound for TC(X) .-16 Examples .-17 Simultaneous control of many systems.-18 Another inequality relating TC(X) to the usual category .-19 Topological complexity of bouquets.-20 A general recipe to construct a motion planning algorithm.-21 How difficult is to avoid collisions in $mathbb$m? .-22 The case m = 2.- 23 TC(F($mathbb$m; n) in the case m $geq$ 3 odd .- 24 Shade.-25 Illuminating the complement of the braid arrangement .-26 A quadratic motion planning algorithm in F($mathbb$m; n).-27