  Approximate query processing (AQP) is an interesting alternative for exact
query processing. It is a tool for dealing with the huge data volumes where
response time is more important than perfect accuracy (this is typically the
case during initial phase of data exploration). There are many techniques for
AQP, one of them is based on probability density functions (PDF). PDFs are
typically calculated using nonparametric data-driven methods. One of the most
popular nonparametric method is the kernel density estimator (KDE). However, a
very serious drawback of using KDEs is the large number of calculations
required to compute them. The shape of final density function is very sensitive
to an entity called bandwidth or smoothing parameter. Calculating it's optimal
value is not a trivial task and in general is very time consuming. In this
paper we investigate the possibility of utilizing two SIMD architectures: SSE
CPU extensions and NVIDIA's CUDA architecture to accelerate finding of the
bandwidth. Our experiments show orders of magnitude improvements over a simple
sequential implementation of classical algorithms used for that task.
