A complete, self-contained introduction to a powerful and resurging mathematical discipline . Combinatorial Geometry presents and explains with complete proofs some of the most important results and methods of this relatively young mathematical discipline, started by Minkowski, Fejes Toth, Rogers, and Erd s. Nearly half the results presented in this book were discovered over the past twenty years, and most have never before appeared in any monograph. Combinatorial Geometry will be of particular interest to mathematicians, computer scientists, physicists, and materials scientists interested in...

Applications of Davenport-Schinzel sequences arise in areas as diverse as robot motion planning, computer graphics and vision, and pattern matching. These sequences exhibit some surprising properties that make them a fascinating subject for research in combinatorial analysis. This book provides a comprehensive study of the combinatorial properties of Davenport-Schinzel sequences and their numerous geometric applications. These sequences are sophisticated tools for solving problems in computational and combinatorial geometry. This first book on the subject by two of its leading researchers...

Applications of Davenport-Schinzel sequences arise in areas as diverse as robot motion planning, computer graphics and vision, and pattern matching. These sequences exhibit some surprising properties that make them a fascinating subject for research in combinatorial analysis. This book provides a comprehensive study of the combinatorial properties of Davenport-Schinzel sequences and their numerous geometric applications. These sequences are sophisticated tools for solving problems in computational and combinatorial geometry. This first book on the subject by two of its leading researchers...

This book presents a study of various problems related to arrangements of lines, segments, or curves in the plane. The first problem is a proof of almost tight bounds on the length of (n, s)-Davenport-Schinzel sequences, a technique for obtaining optimal bounds for numerous algorithmic problems. Then the intersection problem is treated. The final problem is improving the efficiency of partitioning algorithms, particularly those used to construct spanning trees with low stabbing numbers, a very versatile tool in solving geometric problems. A number of applications are also discussed.

This volume gathers together cutting-edge research from the Third Workshop on Algorithmic Foundations of Robotics and gives a solid overview of the state of the art in robot algorithms. The papers cover core problems in robotics, such as motion planning, sensor-based planning, manipulation, and assembly planning. They also examine the application of robotic algorithms in domains like molecular modeling, geometric modeling, and computer-assisted surgery.

This book presents a study of various problems related to arrangements of lines, segments, or curves in the plane. The first problem is a proof of almost tight bounds on the length of (n, s)-Davenport-Schinzel sequences, a technique for obtaining optimal bounds for numerous algorithmic problems. Then the intersection problem is treated. The final problem is improving the efficiency of partitioning algorithms, particularly those used to construct spanning trees with low stabbing numbers, a very versatile tool in solving geometric problems. A number of applications are also discussed.