This symposium is jointly sponsored by the ACM Special Interest Group on Algorithms and Computation Theory and the SIAM Activity Group on Discrete Mathematics.

Leave nothing to chance. This cliche embodies the common belief that ran domness has no place in carefully planned methodologies, every step should be spelled out, each i dotted and each t crossed. In discrete mathematics at least, nothing could be further from the truth. Introducing random choices into algorithms can improve their performance. The application of proba bilistic tools has led to the resolution of combinatorial problems which had resisted attack for decades. The chapters in this volume explore and celebrate this fact. Our intention was to bring together, for the first time, accessible discus sions of the disparate ways in which probabilistic ideas are enriching discrete mathematics. These discussions are aimed at mathematicians with a good combinatorial background but require only a passing acquaintance with the basic definitions in probability (e.g. expected value, conditional probability). A reader who already has a firm grasp on the area will be interested in the original research, novel syntheses, and discussions of ongoing developments scattered throughout the book. Some of the most convincing demonstrations of the power of these tech niques are randomized algorithms for estimating quantities which are hard to compute exactly. One example is the randomized algorithm of Dyer, Frieze and Kannan for estimating the volume of a polyhedron. To illustrate these techniques, we consider a simple related problem. Suppose S is some region of the unit square defined by a system of polynomial inequalities: Pi (x. y) ~ o.

Symposium held in Miami, Florida, January 22–24, 2006.This symposium is jointly sponsored by the ACM Special Interest Group on Algorithms and Computation Theory and the SIAM Activity Group on Discrete Mathematics.Contents Preface; Acknowledgments; Session 1A: Confronting Hardness Using a Hybrid Approach, Virginia Vassilevska, Ryan Williams, and Shan Leung Maverick Woo; A New Approach to Proving Upper Bounds for MAX-2-SAT, Arist Kojevnikov and Alexander S. Kulikov, Measure and Conquer: A Simple O(20.288n) Independent Set Algorithm, Fedor V. Fomin, Fabrizio Grandoni, and Dieter Kratsch; A Polynomial Algorithm to Find an Independent Set of Maximum Weight in a Fork-Free Graph, Vadim V. Lozin and Martin Milanic; The Knuth-Yao Quadrangle-Inequality Speedup is a Consequence of Total-Monotonicity, Wolfgang W. Bein, Mordecai J. Golin, Larry L. Larmore, and Yan Zhang; Session 1B: Local Versus Global Properties of Metric Spaces, Sanjeev Arora, László Lovász, Ilan Newman, Yuval Rabani, Yuri Rabinovich, and Santosh Vempala; Directed Metrics and Directed Graph Partitioning Problems, Moses Charikar, Konstantin Makarychev, and Yury Makarychev; Improved Embeddings of Graph Metrics into Random Trees, Kedar Dhamdhere, Anupam Gupta, and Harald Räcke; Small Hop-diameter Sparse Spanners for Doubling Metrics, T-H. Hubert Chan and Anupam Gupta; Metric Cotype, Manor Mendel and Assaf Naor; Session 1C: On Nash Equilibria for a Network Creation Game, Susanne Albers, Stefan Eilts, Eyal Even-Dar, Yishay Mansour, and Liam Roditty; Approximating Unique Games, Anupam Gupta and Kunal Talwar; Computing Sequential Equilibria for Two-Player Games, Peter Bro Miltersen and Troels Bjerre Sørensen; A Deterministic Subexponential Algorithm for Solving Parity Games, Marcin Jurdzinski, Mike Paterson, and Uri Zwick; Finding Nucleolus of Flow Game, Xiaotie Deng, Qizhi Fang, and Xiaoxun Sun, Session 2: Invited Plenary Abstract: Predicting the “Unpredictable”, Rakesh V. Vohra, Northwestern University; Session 3A: A Near-Tight Approximation Lower Bound and Algorithm for the Kidnapped Robot Problem, Sven Koenig, Apurva Mudgal, and Craig Tovey; An Asymptotic Approximation Algorithm for 3D-Strip Packing, Klaus Jansen and Roberto Solis-Oba; Facility Location with Hierarchical Facility Costs, Zoya Svitkina and Éva Tardos; Combination Can Be Hard: Approximability of the Unique Coverage Problem, Erik D. Demaine, Uriel Feige, Mohammad Taghi Hajiaghayi, and Mohammad R. Salavatipour; Computing Steiner Minimum Trees in Hamming Metric, Ernst Althaus and Rouven Naujoks; Session 3B: Robust Shape Fitting via Peeling and Grating Coresets, Pankaj K. Agarwal, Sariel Har-Peled, and Hai Yu; Tightening Non-Simple Paths and Cycles on Surfaces, Éric Colin de Verdière and Jeff Erickson; Anisotropic Surface Meshing, Siu-Wing Cheng, Tamal K. Dey, Edgar A. Ramos, and Rephael Wenger; Simultaneous Diagonal Flips in Plane Triangulations, Prosenjit Bose, Jurek Czyzowicz, Zhicheng Gao, Pat Morin, and David R. Wood; Morphing Orthogonal Planar Graph Drawings, Anna Lubiw, Mark Petrick, and Michael Spriggs; Session 3C: Overhang, Mike Paterson and Uri Zwick; On the Capacity of Information Networks, Micah Adler, Nicholas J. A. Harvey, Kamal Jain, Robert Kleinberg, and April Rasala Lehman; Lower Bounds for Asymmetric Communication Channels and Distributed Source Coding, Micah Adler, Erik D. Demaine, Nicholas J. A. Harvey, and Mihai Patrascu; Self-Improving Algorithms, Nir Ailon, Bernard Chazelle, Seshadhri Comandur, and Ding Liu; Cake Cutting Really is Not a Piece of Cake, Jeff Edmonds and Kirk Pruhs; Session 4A: Testing Triangle-Freeness in General Graphs, Noga Alon, Tali Kaufman, Michael Krivelevich, and Dana Ron; Constraint Solving via Fractional Edge Covers, Martin Grohe and Dániel Marx; Testing Graph Isomorphism, Eldar Fischer and Arie Matsliah; Efficient Construction of Unit Circular-Arc Models, Min Chih Lin and Jayme L. Szwarcfiter, On The Chromatic Number of Some Geometric Hypergraphs, Shakhar Smorodinsky; Session 4B: A Robust Maximum Completion Time Measure for Scheduling, Moses Charikar and Samir Khuller; Extra Unit-Speed Machines are Almost as Powerful as Speedy Machines for Competitive Flow Time Scheduling, Ho-Leung Chan, Tak-Wah Lam, and Kin-Shing Liu; Improved Approximation Algorithms for Broadcast Scheduling, Nikhil Bansal, Don Coppersmith, and Maxim Sviridenko; Distributed Selfish Load Balancing, Petra Berenbrink, Tom Friedetzky, Leslie Ann Goldberg, Paul Goldberg, Zengjian Hu, and Russell Martin; Scheduling Unit Tasks to Minimize the Number of Idle Periods: A Polynomial Time Algorithm for Offline Dynamic Power Management, Philippe Baptiste; Session 4C: Rank/Select Operations on Large Alphabets: A Tool for Text Indexing, Alexander Golynski, J. Ian Munro, and S. Srinivasa Rao; O(log log n)-Competitive Dynamic Binary Search Trees, Chengwen Chris Wang, Jonathan Derryberry, and Daniel Dominic Sleator; The Rainbow Skip Graph: A Fault-Tolerant Constant-Degree Distributed Data Structure, Michael T. Goodrich, Michael J. Nelson, and Jonathan Z. Sun; Design of Data Structures for Mergeable Trees, Loukas Georgiadis, Robert E. Tarjan, and Renato F. Werneck; Implicit Dictionaries with O(1) Modifications per Update and Fast Search, Gianni Franceschini and J. Ian Munro; Session 5A: Sampling Binary Contingency Tables with a Greedy Start, Ivona Bezáková, Nayantara Bhatnagar, and Eric Vigoda; Asymmetric Balanced Allocation with Simple Hash Functions, Philipp Woelfel; Balanced Allocation on Graphs, Krishnaram Kenthapadi and Rina Panigrahy; Superiority and Complexity of the Spaced Seeds, Ming Li, Bin Ma, and Louxin Zhang; Solving Random Satisfiable 3CNF Formulas in Expected Polynomial Time, Michael Krivelevich and Dan Vilenchik; Session 5B: Analysis of Incomplete Data and an Intrinsic-Dimension Helly Theorem, Jie Gao, Michael Langberg, and Leonard J. Schulman; Finding Large Sticks and Potatoes in Polygons, Olaf Hall-Holt, Matthew J. Katz, Piyush Kumar, Joseph S. B. Mitchell, and Arik Sityon; Randomized Incremental Construction of Three-Dimensional Convex Hulls and Planar Voronoi Diagrams, and Approximate Range Counting, Haim Kaplan and Micha Sharir; Vertical Ray Shooting and Computing Depth Orders for Fat Objects, Mark de Berg and Chris Gray; On the Number of Plane Graphs, Oswin Aichholzer, Thomas Hackl, Birgit Vogtenhuber, Clemens Huemer, Ferran Hurtado, and Hannes Krasser; Session 5C: All-Pairs Shortest Paths for Unweighted Undirected Graphs in o(mn) Time, Timothy M. Chan; An O(n log n) Algorithm for Maximum st-Flow in a Directed Planar Graph, Glencora Borradaile and Philip Klein; A Simple GAP-Canceling Algorithm for the Generalized Maximum Flow Problem, Mateo Restrepo and David P. Williamson; Four Point Conditions and Exponential Neighborhoods for Symmetric TSP, Vladimir Deineko, Bettina Klinz, and Gerhard J. Woeginger; Upper Degree-Constrained Partial Orientations, Harold N. Gabow; Session 7A: On the Tandem Duplication-Random Loss Model of Genome Rearrangement, Kamalika Chaudhuri, Kevin Chen, Radu Mihaescu, and Satish Rao; Reducing Tile Complexity for Self-Assembly Through Temperature Programming, Ming-Yang Kao and Robert Schweller; Cache-Oblivious String Dictionaries, Gerth Stølting Brodal and Rolf Fagerberg; Cache-Oblivious Dynamic Programming, Rezaul Alam Chowdhury and Vijaya Ramachandran; A Computational Study of External-Memory BFS Algorithms, Deepak Ajwani, Roman Dementiev, and Ulrich Meyer; Session 7B: Tight Approximation Algorithms for Maximum General Assignment Problems, Lisa Fleischer, Michel X. Goemans, Vahab S. Mirrokni, and Maxim Sviridenko; Approximating the k-Multicut Problem, Daniel Golovin, Viswanath Nagarajan, and Mohit Singh; The Prize-Collecting Generalized Steiner Tree Problem Via A New Approach Of Primal-Dual Schema, Mohammad Taghi Hajiaghayi and Kamal Jain; 8/7-Approximation Algorithm for (1,2)-TSP, Piotr Berman and Marek Karpinski; Improved Lower and Upper Bounds for Universal TSP in Planar Metrics, Mohammad T. Hajiaghayi, Robert Kleinberg, and Tom Leighton; Session 7C: Leontief Economies Encode NonZero Sum Two-Player Games, B. Codenotti, A. Saberi, K. Varadarajan, and Y. Ye; Bottleneck Links, Variable Demand, and the Tragedy of the Commons, Richard Cole, Yevgeniy Dodis, and Tim Roughgarden; The Complexity of Quantitative Concurrent Parity Games, Krishnendu Chatterjee, Luca de Alfaro, and Thomas A. Henzinger; Equilibria for Economies with Production: Constant-Returns Technologies and Production Planning Constraints, Kamal Jain and Kasturi Varadarajan; Session 8A: Approximation Algorithms for Wavelet Transform Coding of Data Streams, Sudipto Guha and Boulos Harb; Simpler Algorithm for Estimating Frequency Moments of Data Streams, Lakshimath Bhuvanagiri, Sumit Ganguly, Deepanjan Kesh, and Chandan Saha; Trading Off Space for Passes in Graph Streaming Problems, Camil Demetrescu, Irene Finocchi, and Andrea Ribichini; Maintaining Significant Stream Statistics over Sliding Windows, L.K. Lee and H.F. Ting; Streaming and Sublinear Approximation of Entropy and Information Distances, Sudipto Guha, Andrew McGregor, and Suresh Venkatasubramanian; Session 8B: FPTAS for Mixed-Integer Polynomial Optimization with a Fixed Number of Variables, J. A. De Loera, R. Hemmecke, M. Köppe, and R. Weismantel; Linear Programming and Unique Sink Orientations, Bernd Gärtner and Ingo Schurr; Generating All Vertices of a Polyhedron is Hard, Leonid Khachiyan, Endre Boros, Konrad Borys, Khaled Elbassioni, and Vladimir Gurvich; A Semidefinite Programming Approach to Tensegrity Theory and Realizability of Graphs, Anthony Man-Cho So and Yinyu Ye; Ordering by Weighted Number of Wins Gives a Good Ranking for Weighted Tournaments, Don Coppersmith, Lisa Fleischer, and Atri Rudra; Session 8C: Weighted Isotonic Regression under L1 Norm, Stanislav Angelov, Boulos Harb, Sampath Kannan, and Li-San Wang; Oblivious String Embeddings and Edit Distance Approximations, Tugkan Batu, Funda Ergun, and Cenk Sahinalp0898716012\\This comprehensive book not only introduces the C and C++ programming languages but also shows how to use them in the numerical solution of partial differential equations (PDEs). It leads the reader through the entire solution process, from the original PDE, through the discretization stage, to the numerical solution of the resulting algebraic system. The well-debugged and tested code segments implement the numerical methods efficiently and transparently. Basic and advanced numerical methods are introduced and implemented easily and efficiently in a unified object-oriented approach.

Handbook of Approximation Algorithms and Metaheuristics, Second Edition reflects the tremendous growth in the field, over the past two decades. Through contributions from leading experts, this handbook provides a comprehensive introduction to the underlying theory and methodologies, as well as the various applications of approximation algorithms and metaheuristics. Volume 1 of this two-volume set deals primarily with methodologies and traditional applications. It includes restriction, relaxation, local ratio, approximation schemes, randomization, tabu search, evolutionary computation, local search, neural networks, and other metaheuristics. It also explores multi-objective optimization, reoptimization, sensitivity analysis, and stability. Traditional applications covered include: bin packing, multi-dimensional packing, Steiner trees, traveling salesperson, scheduling, and related problems. Volume 2 focuses on the contemporary and emerging applications of methodologies to problems in combinatorial optimization, computational geometry and graphs problems, as well as in large-scale and emerging application areas. It includes approximation algorithms and heuristics for clustering, networks (sensor and wireless), communication, bioinformatics search, streams, virtual communities, and more. About the Editor Teofilo F. Gonzalez is a professor emeritus of computer science at the University of California, Santa Barbara. He completed his Ph.D. in 1975 from the University of Minnesota. He taught at the University of Oklahoma, the Pennsylvania State University, and the University of Texas at Dallas, before joining the UCSB computer science faculty in 1984. He spent sabbatical leaves at the Monterrey Institute of Technology and Higher Education and Utrecht University. He is known for his highly cited pioneering research in the hardness of approximation; for his sublinear and best possible approximation algorithm for k-tMM clustering; for introducing the open-shop scheduling problem as well as algorithms for its solution that have found applications in numerous research areas; as well as for his research on problems in the areas of job scheduling, graph algorithms, computational geometry, message communication, wire routing, etc.

Contains 130 papers, which were selected based on originality, technical contribution, and relevance. Although the papers were not formally refereed, every attempt was made to verify the main claims. It is expected that most will appear in more complete form in scientific journals. The proceedings also includes the paper presented by invited plenary speaker Ronald Graham, as well as a portion of the papers presented by invited plenary speakers Udi Manber and Christos Papadimitriou.

This book constitutes the refereed proceedings of the 15th Annual European Symposium on Algorithms, ESA 2007, held in Eilat, Israel, in October 2007 in the context of the combined conference ALGO 2007. The 63 revised full papers presented together with abstracts of three invited lectures address all current subjects in algorithmics reaching from design and analysis issues of algorithms over to real-world applications and engineering of algorithms in various fields.

One of Springer’s renowned Major Reference Works, this awesome achievement provides a comprehensive set of solutions to important algorithmic problems for students and researchers interested in quickly locating useful information. This first edition of the reference focuses on high-impact solutions from the most recent decade, while later editions will widen the scope of the work. All entries have been written by experts, while links to Internet sites that outline their research work are provided. The entries have all been peer-reviewed. This defining reference is published both in print and on line.

This book constitutes the refereed proceedings of the 10th International Conference on Parallel Computing, Euro-Par 2004, held in Pisa, Italy in August/September 2004. The 122 revised papers presented together with 3 invited papers were carefully reviewed and selected from 352 submissions. The papers are organized in topical sections on support tools and environments, performance evaluation, scheduling and load balancing, compilers and high performance, parallel and distributed databases, grid and cluster computing, applications on high performance clusters, parallel computer architecture and ILP, distributed systems and algorithms, parallel programming, numerical algorithms, high performance multimedia, theory and algorithms for parallel computing, routing and communication in interconnection networks, mobile computing, integrated problem solving environments, high performance bioinformatics, and peer-to-peer and Web computing.

This little book is conceived as a service to mathematicians attending the 1998 International Congress of Mathematicians in Berlin. It presents a comprehensive, condensed overview of mathematical activity in Berlin, from Leibniz almost to the present day (without, however, including biographies of living mathematicians). Since many towering figures in mathematical history worked in Berlin, most of the chapters of this book are concise biographies. These are held together by a few survey articles presenting the overall development of entire periods of scientific life at Berlin. Overlaps between various chapters and differences in style between the chap ters were inevitable, but sometimes this provided opportunities to show different aspects of a single historical event - for instance, the Kronecker-Weierstrass con troversy. The book aims at readability rather than scholarly completeness. There are no footnotes, only references to the individual bibliographies of each chapter. Still, we do hope that the texts brought together here, and written by the various authors for this volume, constitute a solid introduction to the history of Berlin mathematics.

The Steiner tree problem is one of the most important combinatorial optimization problems. It has a long history that can be traced back to the famous mathematician Fermat (1601-1665). This book studies three significant breakthroughs on the Steiner tree problem that were achieved in the 1990s, and some important applications of Steiner tree problems in computer communication networks researched in the past fifteen years. It not only covers some of the most recent developments in Steiner tree problems, but also discusses various combinatorial optimization methods, thus providing a balance between theory and practice. Sample Chapter(s). Chapter 1: Minimax Approach and Steiner Ratio (372 KB). Contents: Minimax Approach and Steiner Ratio; k -Steiner Ratios and Better Approximation Algorithms; Geometric Partitions and Polynomial Time Approximation Schemes; Grade of Service Steiner Tree Problem; Steiner Tree Problem for Minimal Steiner Points; Bottleneck Steiner Tree Problem; Steiner k -Tree and k -Path Routing Problems; Steiner Tree Coloring Problem; Steiner Tree Scheduling Problem; Survivable Steiner Network Problem. Readership: Researchers and graduate students of computer science and engineering as well as operations research.