We are motivated by an optimization problem arising in computational scaling for optical lithography that reduces to finding the point of minimum radius that lies outside of the union of a set of diamonds centered at the origin of Euclidean space of arbitrary dimension. A decomposition of the feasible region into convex regions suggests a heuristic sampling approach to finding the global minimum. We describe a technique for decomposing the surface of a hypersphere of arbitrary dimension, both exactly and approximately, into a specific number of regions of equal area and small diameter. The decomposition generalizes to any problem posed on a spherical domain where regularity of the decomposition is an important concern. We specifically consider a storage-optimized decomposition and analyze its performance. We also show how the decomposition can parallelize the sampling process by assigning each processor a subset of points on the hypersphere to sample. Finally, we describe a freely available C++ software package that implements the storage-optimized decomposition. © 2009 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Ahmadia, A., Keyes, D., Melville, D., Rosenbluth, A., & Tian, K. (2009). Distributed decomposition over hyperspherical domains. In Lecture Notes in Computational Science and Engineering (Vol. 70 LNCSE, pp. 251–258). https://doi.org/10.1007/978-3-642-02677-5_27
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