This text covers the proceedings of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, which was held in Atlanta, Georgia, in January 1996.

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

Annotation This volume contains 93 traditional papers and 74 short form abstracts presented at the January 1999 symposium, which encouraged increased participation from the discrete mathematics community this year. Topics of the longer papers include page replacement for general caching problems, queries with segments in Voronoi diagrams, clustering in large graphs and matrices, the complexity of gene placement, and indexing schemes for random points. Some of the short paper topics are locked and unlocked polygonal chains in 3D, compact roundtrip routing for digraphs, and sampling spin configurations on an Ising system. No subject index. Annotation copyrighted by Book News, Inc., Portland, OR.

This book describes in detail sampling techniques that can be used for unsupervised and supervised cases, with a focus on sampling techniques for machine learning algorithms. It covers theory and models of sampling methods for managing scalability and the “curse of dimensionality”, their implementations, evaluations, and applications. A large part of the book is dedicated to database comprising standard feature vectors, and a special section is reserved to the handling of more complex objects and dynamic scenarios. The book is ideal for anyone teaching or learning pattern recognition and interesting teaching or learning pattern recognition and is interested in the big data challenge. It provides an accessible introduction to the field and discusses the state of the art concerning sampling techniques for supervised and unsupervised task. Provides a comprehensive description of sampling techniques for unsupervised and supervised tasks; Describe implementation and evaluation of algorithms that simultaneously manage scalable problems and curse of dimensionality; Addresses the role of sampling in dynamic scenarios, sampling when dealing with complex objects, and new challenges arising from big data. "This book represents a timely collection of state-of-the art research of sampling techniques, suitable for anyone who wants to become more familiar with these helpful techniques for tackling the big data challenge." M. Emre Celebi, Ph.D., Professor and Chair, Department of Computer Science, University of Central Arkansas "In science the difficulty is not to have ideas, but it is to make them work" From Carlo Rovelli

Nash equilibrium is the central solution concept in Game Theory. Since Nash’s original paper in 1951, it has found countless applications in modeling strategic behavior of traders in markets, (human) drivers and (electronic) routers in congested networks, nations in nuclear disarmament negotiations, and more. A decade ago, the relevance of this solution concept was called into question by computer scientists, who proved (under appropriate complexity assumptions) that computing a Nash equilibrium is an intractable problem. And if centralized, specially designed algorithms cannot find Nash equilibria, why should we expect distributed, selfish agents to converge to one? The remaining hope was that at least approximate Nash equilibria can be efficiently computed. Understanding whether there is an efficient algorithm for approximate Nash equilibrium has been the central open problem in this field for the past decade. In this book, we provide strong evidence that even finding an approximate Nash equilibrium is intractable. We prove several intractability theorems for different settings (two-player games and many-player games) and models (computational complexity, query complexity, and communication complexity). In particular, our main result is that under a plausible and natural complexity assumption ("Exponential Time Hypothesis for PPAD"), there is no polynomial-time algorithm for finding an approximate Nash equilibrium in two-player games. The problem of approximate Nash equilibrium in a two-player game poses a unique technical challenge: it is a member of the class PPAD, which captures the complexity of several fundamental total problems, i.e., problems that always have a solution; and it also admits a quasipolynomial time algorithm. Either property alone is believed to place this problem far below NP-hard problems in the complexity hierarchy; having both simultaneously places it just above P, at what can be called the frontier of intractability. Indeed, the tools we develop in this book to advance on this frontier are useful for proving hardness of approximation of several other important problems whose complexity lies between P and NP: Brouwer’s fixed point, market equilibrium, CourseMatch (A-CEEI), densest k-subgraph, community detection, VC dimension and Littlestone dimension, and signaling in zero-sum games.

This book constitutes revised selected papers from the 15th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2019, held in Munich, Germany, in September 2019. The 11 full papers presented in this volume were carefully reviewed and selected from 16 submissions. ALGOSENSORS is an international symposium dedicated to the algorithmic aspects of wireless networks.