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1. Graph theory [2010]

Book
xviii, 436 p. : ill. ; 24 cm.
  • The Basics.- Matching Covering and Packing.- Connectivity.- Planar Graphs.- Colouring.- Flows.- Extremal Graph Theory.- Infinite Graphs.- Ramsey Theory for Graphs.- Hamilton Cycles.- Random Graphs.- Minors Trees and WQO.
  • (source: Nielsen Book Data)9783642142789 20160604
Almosttwodecadeshavepassedsincetheappearanceofthosegrapht- ory texts that still set the agenda for most introductory courses taught today. The canon created by those books has helped to identify some main?eldsofstudyandresearch, andwilldoubtlesscontinuetoin?uence the development of the discipline for some time to come. Yet much has happened in those 20 years, in graph theory no less thanelsewhere: deepnewtheoremshavebeenfound, seeminglydisparate methods and results have become interrelated, entire new branches have arisen. To name just a few such developments, one may think of how the new notion of list colouring has bridged the gulf between inva- ants such as average degree and chromatic number, how probabilistic methods andtheregularity lemmahave pervadedextremalgraphtheory and Ramsey theory, or how the entirely new ?eld of graph minors and tree-decompositions has brought standard methods of surface topology to bear on long-standing algorithmic graph problems. Clearly, then, the time has come for a reappraisal: what are, today, the essential areas, methods and results that should form the centre of an introductory graph theory course aiming to equip its audience for the most likely developments ahead? I have tried in this book to o?er material for such a course. In view of the increasing complexity and maturity of the subject, I have broken with the tradition of attempting to cover both theory and app- cations: this book o?ers an introduction to the theory of graphs as part of (pure) mathematics; it contains neither explicit algorithms nor 'real world' applications.
(source: Nielsen Book Data)9783642142789 20160604
Engineering Library (Terman)
CME-305-01, MS&E-316-01
Book
xxi, 754 p. : ill. ; 26 cm.
  • Introduction Noam Nisan, Tim Roughgarden, Eva Tardos and Vijay V. Vazirani-- Part I. Computing in Games: 1. Basic solution concepts and computational issues Eva Tardos and Vijay V. Vazirani-- 2. Algorithms for equilibria Christos Papadimitriou-- 3. Equilibrium computation for games in strategic and extensive form Bernhard von Stengel-- 4. Learning, regret minimization and correlated equilibria Avrim Blum and Yishay Mansour-- 5. Graphical games Michael J. Kearns-- 6. Cryptography and game theory Yevgeniy Dodis and Tal Rabin-- 7. Combinatorial algorithms for market equilibria Vijay V. Vazirani-- 8. Computation of market equilibria by convex programming Bruno Codenotti and Kasturi Varadarajan-- Part II. Algorithmic Mechanism Design: 9. Introduction to mechanism design (for computer scientists) Noam Nisan-- 10. Mechanism design without money James Schummer and Rakesh V. Vohra-- 11. Combinatorial auctions Noam Nisan and Liad Blumrosen-- 12. Computationally efficient approximation mechanisms Ron Lavi-- 13. Profit maximization in mechanism design Jason Hartline and Anna Karlin-- 14. Distributed algorithmic mechanism design Joan Feigenbaum, Michael Schapira and Scott Shenker-- 15. Cost sharing Kamal Jain and Mohammad Mahdian-- 16. On-line mechanisms David C. Parkes-- Part III. Quantifying the Inefficiency of Equilibria: 17. Introduction to the inefficiency of equilibria Tim Roughgarden and Eva Tardos-- 18. Routing games Tim Roughgarden-- 19. Inefficiency of equilibria in network formation games Eva Tardos and Tom Wexler-- 20. Selfish load-balancing Berthold Vocking-- 21. Efficiency loss and the design of scalable resource allocation mechanisms Ramesh Johari-- Part IV. Additional Topics: 22. Incentives and pricing in communication networks Asuman Ozdaglar and R. Srikant-- 23. Incentives in peer-to-peer systems John Chuang, Michal Feldman and Moshe Babaioff-- 24. Cascading behavior in networks: algorithmic and economic issues Jon Kleinberg-- 25. Incentives and information security Ross Anderson, Tyler Moore, Shishir Nagaraja and Andy Ozment-- 26. Computational aspects of information markets David M. Pennock and Rahul Sami-- 27. Manipulation-resistant reputation systems Eric Friedman, Paul Resnick and Rahul Sami-- 28. Sponsored search auctions Sebastien Lahaie, David M. Pennock, Amin Saberi and Rakesh V. Vohra-- 29. Algorithmic issues in evolutionary game theory Michael Kearns and Siddharth Suri.
  • (source: Nielsen Book Data)9780521872829 20160528
In the last few years game theory has had a substantial impact on computer science, especially on Internet- and e-commerce-related issues. Algorithmic Game Theory develops the central ideas and results of this new and exciting area in a clear and succinct manner. More than 40 of the top researchers in this field have written chapters that go from the foundations to the state of the art. Basic chapters on algorithmic methods for equilibria, mechanism design and combinatorial auctions are followed by chapters on important game theory applications such as incentives and pricing, cost sharing, information markets and cryptography and security. This definitive work will set the tone of research for the next few years and beyond. Students, researchers, and practitioners alike need to learn more about these fascinating theoretical developments and their widespread practical application.
(source: Nielsen Book Data)9780521872829 20160528
Engineering Library (Terman), eReserve
CME-305-01, MS&E-316-01

3. Algorithm design [2006]

Book
xxiii, 838 p. : ill. ; 24 cm.
  • 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 Greedy Algorithms 4.1 Interval Scheduling: The Greedy Algorithm Stays Ahead 4.2 Scheduling to Minimize Lateness: An Exchange Argument 4.3 Optimal Caching: A More Complex Exchange Argument 4.4 Shortest Paths in a Graph 4.5 The Minimum Spanning Tree Problem 4.6 Implementing Kruskal's Algorithm: The Union-Find Data Structure 4.7 Clustering 4.8 Huffman Codes and the Problem of Data Compression *4.9 Minimum-Cost Arborescences: A Multi-Phase Greedy Algorithm Solved Exercises Excercises Notes and Further Reading 5 Divide and Conquer 5.1 A First Recurrence: The Mergesort Algorithm 5.2 Further Recurrence Relations 5.3 Counting Inversions 5.4 Finding the Closest Pair of Points 5.5 Integer Multiplication 5.6 Convolutions and The Fast Fourier Transform Solved Exercises Exercises 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 Problem in Polynomial Space 9.5 Proving Problems PSPACE-Complete Solved Exercises Exercises Notes 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 Reading 11 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 Exercises Exercises Notes and Further Reading 12 Local Search 12.1 The Landscape of an Optimization Problem 12.2 The Metropolis Algorithm and Simulated Annealing 12.3 An Application of Local Search to Hopfield Neural Networks 12.4 Maximum Cut Approximation via Local Search 12.5 Choosing a Neighbor Relation *12.6 Classification via Local Search 12.7 Best-Response Dynamics and Nash Equilibria Solved Exercises Exercises Notes and Further Reading 13 Randomized Algorithms 13.1 A First Application: Contention Resolution 13.2 Finding the Global Minimum Cut 13.3 Random Variables and their Expectations 13.4 A Randomized Approximation Algorithm for MAX 3-SAT 13.5 Randomized Divide-and-Conquer: Median-Finding and Quicksort 13.6 Hashing: A Randomized Implementation of Dictionaries 13.7 Finding the Closest Pair of Points: A Randomized Approach 13.8 Randomized Caching 13.9 Chernoff Bounds 13.10 Load Balancing *13.11 Packet Routing 13.12 Background: Some Basic Probability Definitions Solved Exercises Exercises Notes and Further Reading Epilogue: Algorithms that Run Forever References Index.
  • (source: Nielsen Book Data)9780321295354 20160528
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.
(source: Nielsen Book Data)9780321295354 20160528
Engineering Library (Terman)
CME-305-01, MS&E-316-01
Book
476 p.
  • Part I. Tools and Techniques: 1. Introduction-- 2. Game-theoretic techniques-- 3. Moments and deviations-- 4. Tail inequalities-- 5. The probabilistic method-- 6. Markov chains and random walks-- 7. Algebraic techniques-- Part II. Applications: 8. Data structures-- 9. Geometric algorithms and linear programming-- 10. Graph algorithms-- 11. Approximate counting-- 12. Parallel and distributed algorithms-- 13. Online algorithms-- 14. Number theory and algebra-- Appendix A: notational index-- Appendix B: mathematical background-- Appendix C: basic probability theory.
  • (source: Nielsen Book Data)9780521474658 20160528
For many applications a randomized algorithm is either the simplest algorithm available, or the fastest, or both. This tutorial presents the basic concepts in the design and analysis of randomized algorithms. The first part of the book presents tools from probability theory and probabilistic analysis that are recurrent in algorithmic applications. Algorithmic examples are given to illustrate the use of each tool in a concrete setting. In the second part of the book, each of the seven chapters focuses on one important area of application of randomized algorithms: data structures; geometric algorithms; graph algorithms; number theory; enumeration; parallel algorithms; and on-line algorithms. A comprehensive and representative selection of the algorithms in these areas is also given. This first book on the subject should prove invaluable as a reference for researchers and professional programmers, as well as for students.
(source: Nielsen Book Data)9780521474658 20160528
Engineering Library (Terman), eReserve
CME-305-01, MS&E-316-01