in an extension of CTL with clock variables). We develop an algorithm that computes this set of states symbolically as a fixpoint of a functional on state predicates, without constructing the state space. For this purpose, we introduce a -calculus on computation trees over real-numbered time. Unfortunately

We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized

The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new site in O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are simple enough to be of practical value. The simplicity of both algorithms can be attributed to the separation of the geometrical and topological aspects of the problem and to the use of two simple but powerful primitives, a geometric predicate and an operator for manipulating the topology of the diagram. The topology is represented by a new data structure for generalized diagrams, that is, embeddings of graphs in two-dimensional manifolds. This structure represents simultaneously an embedding, its dual, and its mirror image. Furthermore, just two operators are sufficient for building and modifying arbitrary diagrams.

fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes

Volume rendering is a technique for visualizing 3D arrays of sampled data. It has applications in areas such as medical imaging and scientific visualization, but its use has been limited by its high computational expense. Early implementations of volume rendering used brute-force techniques

This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning

the rapidly developing systematic connections between FPT and useful heuristic algorithms | a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs

In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a

Abstract not found

Abstract not found