004 Datenverarbeitung; Informatik
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We contribute to the theoretical understanding of randomized search heuristics by investigating their optimization behavior on satisfiable random k-satisfiability instances both in the planted solution model and the uniform model conditional on satisfiability. Denoting the number of variables by n, our main technical result is that the simple () evolutionary algorithm with high probability finds a satisfying assignment in time when the clause-variable density is at least logarithmic. For low density instances, evolutionary algorithms seem to be less effective, and all we can show is a subexponential upper bound on the runtime for densities below . We complement these mathematical results with numerical experiments on a broader density spectrum. They indicate that, indeed, the () EA is less efficient on lower densities. Our experiments also suggest that the implicit constants hidden in our main runtime guarantee are low. Our main result extends and considerably improves the result obtained by Sutton and Neumann (Lect Notes Comput Sci 8672:942-951, 2014) in terms of runtime, minimum density, and clause length. These improvements are made possible by establishing a close fitness-distance correlation in certain parts of the search space. This approach might be of independent interest and could be useful for other average-case analyses of randomized search heuristics. While the notion of a fitness-distance correlation has been around for a long time, to the best of our knowledge, this is the first time that fitness-distance correlation is explicitly used to rigorously prove a performance statement for an evolutionary algorithm.
3D point clouds are a digital representation of our world and used in a variety of applications. They are captured with LiDAR or derived by image-matching approaches to get surface information of objects, e.g., indoor scenes, buildings, infrastructures, cities, and landscapes. We present novel interaction and visualization techniques for heterogeneous, time variant, and semantically rich 3D point clouds. Interactive and view-dependent see-through lenses are introduced as exploration tools to enhance recognition of objects, semantics, and temporal changes within 3D point cloud depictions. We also develop filtering and highlighting techniques that are used to dissolve occlusion to give context-specific insights. All techniques can be combined with an out-of-core real-time rendering system for massive 3D point clouds. We have evaluated the presented approach with 3D point clouds from different application domains. The results show the usability and how different visualization and exploration tasks can be improved for a variety of domain-specific applications.