Space-Filling Curves

Michael Bader is professor for computer science at Technische Universität München, where he leads a research group on hardware-aware algorithms and software for high performance computing (located at the Leibniz Supercomputing Centre). His focus in research and teaching is on algorithmic challenges imposed by modern computing platforms. A large part of his work is dedicated to exploiting locality properties of space-filling curves for simulation tasks in science and engineering.

• Two Motivating Examples.- How to Construct Space-Filling Curves.- Grammar-Based Description of Space-Filling Curves.- Arithmetic Representation of Space-Filling Curves.- Approximating Polygons.- Sierpinski Curves.- Further Space-Filling Curves.- Space-Filling Curves in 3D.- Refinement Trees and Space-Filling Curves.- Parallelisation with Space-Filling Curves.- Locality Properties of Space-Filling Curves.- Sierpinski Curves on Triangular and Tetrahedral Meshes.- Case Study: Cache Efficient Algorithms for Matrix Operations.- Case Study: Numerical Simulation on Spacetree Grids Using Space-Filling Curves.- Further Applications of Space-Filling Curves.- Solutions to Selected Exercises.- References.- Index ​

From the reviews:“This book concentrates on low-dimensional, two or three at most, curves used for linearly ordering points on the 2D or 3D grid with applications in computer graphics and data structures. … Each section ends with indications for further reading and exercises. This is a new book in the field of computer science which should be a valuable resource for advanced undergraduate and graduate students as well as more experienced researchers.” (Ewa Skubalska-Rafajłowicz, Mathematical Reviews, January, 2014)“Bader’s book … provides an introduction to the algorithmics of space-filling curves. … The book has many color illustrations and can be used as a textbook and as reference monograph for research.” (Luiz Henrique de Figueiredo, MAA Reviews, April, 2013)“This is a gentle introduction to space filling curves. Emphasis is on the representation, implementation and application in computer science. … It is clear that the author has a long teaching experience with this subject. He had found the right balance between motivation, rigor, application, implementation, in just the right pace to take the reader/student along climbing up the hill towards of increasing complexity as academic examples are left and one approaches the real life applications.” (A. Bultheel, The European Mathematical Society, December, 2012)