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Author: Paul Spirakis Publisher: ISBN: 9781332172443 Category : Mathematics Languages : en Pages : 44
Book Description
Excerpt from On the Combinatorial Complexity of Motion Coordination We investigate the complexity of the problem of coordinating the motion of many planar rigid objects in a two dimensional space. Each object has a simple geometrical description (it is a box or a circle). The number of objects to be moved is part of the problem size. The plane where objects move is partitioned into two regions: The region of forbidden points, being a finite union of areas each bounded by a polygonal line, and its complement. During motion, objects are not allowed to overlap or to intersect the region of forbidden points, but they are allowed to be in contact with the boundary of obstacles or other objects. We analyze several variants of the above problem of motion planning and prove that they are NP-hard, in the strong sense. We also consider simple combinatorial planar graph-and-pebble models which capture certain non-geometric aspects of coordinated motion. We provide an algorithm for planning the motion of k.pebbles in an n-vertex planar graph, which is 0(n ). We also show that coordination of motion of n-1 distinct pebbles in an n-vertex graph, from a set of n-I distinct initial to n-1 distinct final positions, can be decided and planned in polynomial time inn. Finally, we show that certain problems of planning the motion of many pebbles, when the motion is nonsymmetric, or when the final positions are required to satisfy a combinatorial property, are NP-hard in the strong sense. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works."
Author: Paul Spirakis Publisher: ISBN: 9781332172443 Category : Mathematics Languages : en Pages : 44
Book Description
Excerpt from On the Combinatorial Complexity of Motion Coordination We investigate the complexity of the problem of coordinating the motion of many planar rigid objects in a two dimensional space. Each object has a simple geometrical description (it is a box or a circle). The number of objects to be moved is part of the problem size. The plane where objects move is partitioned into two regions: The region of forbidden points, being a finite union of areas each bounded by a polygonal line, and its complement. During motion, objects are not allowed to overlap or to intersect the region of forbidden points, but they are allowed to be in contact with the boundary of obstacles or other objects. We analyze several variants of the above problem of motion planning and prove that they are NP-hard, in the strong sense. We also consider simple combinatorial planar graph-and-pebble models which capture certain non-geometric aspects of coordinated motion. We provide an algorithm for planning the motion of k.pebbles in an n-vertex planar graph, which is 0(n ). We also show that coordination of motion of n-1 distinct pebbles in an n-vertex graph, from a set of n-I distinct initial to n-1 distinct final positions, can be decided and planned in polynomial time inn. Finally, we show that certain problems of planning the motion of many pebbles, when the motion is nonsymmetric, or when the final positions are required to satisfy a combinatorial property, are NP-hard in the strong sense. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works."
Author: Steven Michael LaValle Publisher: ISBN: 9780511241338 Category : Algorithms Languages : en Pages : 826
Book Description
Written for computer scientists and engineers with interests in artificial intelligence, robotics, or control theory, this is the only book on this topic that integrates literature from several fields into a coherent source for teaching and reference in applications including robotics, computational biology, computer graphics, manufacturing, aerospace applications, and medicine.
Author: Sanjeev Arora Publisher: Cambridge University Press ISBN: 0521424267 Category : Computers Languages : en Pages : 609
Book Description
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author: Avi Wigderson Publisher: Princeton University Press ISBN: 0691189137 Category : Computers Languages : en Pages : 434
Book Description
An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Author: Jean-Daniel Boissonnat Publisher: Springer Science & Business Media ISBN: 9783540404767 Category : Technology & Engineering Languages : en Pages : 600
Book Description
Selected contributions to the Workshop WAFR 2002, held December 15-17, 2002, Nice, France. This fifth biannual Workshop on Algorithmic Foundations of Robotics focuses on algorithmic issues related to robotics and automation. The design and analysis of robot algorithms raises fundamental questions in computer science, computational geometry, mechanical modeling, operations research, control theory, and associated fields. The highly selective program highlights significant new results such as algorithmic models and complexity bounds. The validation of algorithms, design concepts, or techniques is the common thread running through this focused collection.
Author: J. A. Scott Kelso Publisher: MIT Press ISBN: 9780262611312 Category : Behavior Languages : en Pages : 368
Book Description
foreword by Hermann Haken For the past twenty years Scott Kelso's research has focused on extending the physical concepts of self- organization and the mathematical tools of nonlinear dynamics to understand how human beings (and human brains) perceive, intend, learn, control, and coordinate complex behaviors. In this book Kelso proposes a new, general framework within which to connect brain, mind, and behavior.Kelso's prescription for mental life breaks dramatically with the classical computational approach that is still the operative framework for many newer psychological and neurophysiological studies. His core thesis is that the creation and evolution of patterned behavior at all levels--from neurons to mind--is governed by the generic processes of self-organization. Both human brain and behavior are shown to exhibit features of pattern-forming dynamical systems, including multistability, abrupt phase transitions, crises, and intermittency. Dynamic Patterns brings together different aspects of this approach to the study of human behavior, using simple experimental examples and illustrations to convey essential concepts, strategies, and methods, with a minimum of mathematics. Kelso begins with a general account of dynamic pattern formation. He then takes up behavior, focusing initially on identifying pattern-forming instabilities in human sensorimotor coordination. Moving back and forth between theory and experiment, he establishes the notion that the same pattern-forming mechanisms apply regardless of the component parts involved (parts of the body, parts of the nervous system, parts of society) and the medium through which the parts are coupled. Finally, employing the latest techniques to observe spatiotemporal patterns of brain activity, Kelso shows that the human brain is fundamentally a pattern forming dynamical system, poised on the brink of instability. Self-organization thus underlies the cooperative action of neurons that produces human behavior in all its forms.
Author: Herbert A. Simon Publisher: MIT Press ISBN: 0262537532 Category : Computers Languages : en Pages : 256
Book Description
Herbert Simon's classic work on artificial intelligence in the expanded and updated third edition from 1996, with a new introduction by John E. Laird. Herbert Simon's classic and influential The Sciences of the Artificial declares definitively that there can be a science not only of natural phenomena but also of what is artificial. Exploring the commonalities of artificial systems, including economic systems, the business firm, artificial intelligence, complex engineering projects, and social plans, Simon argues that designed systems are a valid field of study, and he proposes a science of design. For this third edition, originally published in 1996, Simon added new material that takes into account advances in cognitive psychology and the science of design while confirming and extending the book's basic thesis: that a physical symbol system has the necessary and sufficient means for intelligent action. Simon won the Nobel Prize for Economics in 1978 for his research into the decision-making process within economic organizations and the Turing Award (considered by some the computer science equivalent to the Nobel) with Allen Newell in 1975 for contributions to artificial intelligence, the psychology of human cognition, and list processing. The Sciences of the Artificial distills the essence of Simon's thought accessibly and coherently. This reissue of the third edition makes a pioneering work available to a new audience.
Author: Sebastian Thrun Publisher: MIT Press ISBN: 0262201623 Category : Technology & Engineering Languages : en Pages : 668
Book Description
An introduction to the techniques and algorithms of the newest field in robotics. Probabilistic robotics is a new and growing area in robotics, concerned with perception and control in the face of uncertainty. Building on the field of mathematical statistics, probabilistic robotics endows robots with a new level of robustness in real-world situations. This book introduces the reader to a wealth of techniques and algorithms in the field. All algorithms are based on a single overarching mathematical foundation. Each chapter provides example implementations in pseudo code, detailed mathematical derivations, discussions from a practitioner's perspective, and extensive lists of exercises and class projects. The book's Web site, www.probabilistic-robotics.org, has additional material. The book is relevant for anyone involved in robotic software development and scientific research. It will also be of interest to applied statisticians and engineers dealing with real-world sensor data.
Author: Paul Spirakis
Author: Paul Spirakis
Author: Courant Institute of Mathematical Sciences. Computer Science Department
Author: Steven Michael LaValle
Author: Sanjeev Arora
Author: Avi Wigderson
Author: Jean-Daniel Boissonnat
Author: J. A. Scott Kelso
Author: Roman Vershynin
Author: Herbert A. Simon
Author: Sebastian Thrun