The Probability Density Function (PDF) is a key concept in statistics. Constructing the most adequate PDF from the observed data is still an important and interesting scientific problem, especially for large datasets. PDFs are often estimated 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, especially to find the optimal bandwidth parameter. In this paper we investigate the possibility of utilizing Graphics Processing Units (GPUs) to accelerate the finding of the bandwidth. The contribution of this paper is threefold: (a) we propose algorithmic optimization to one of bandwidth finding algorithms, (b) we propose efficient GPU versions of three bandwidth finding algorithms and (c) we experimentally compare three of our GPU implementations with the ones which utilize only CPUs. Our experiments show orders of magnitude improvements over CPU implementations of classical algorithms.

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This article tackles the problem of efficient construction of iCPI trees, frequently used in co-location pattern discovery in spatial databases. It discusses the methods for parallelization of iCPI-tree construction and plane-sweep algorithms used in state-of-the-art algorithms for co-location pattern mining. The main contribution of this paper is threefold: (1) a general algorithm for parallel iCPI-tree construction is presented, (2) two variants of parallel plane-sweep algorithm (which can be used in conjunction with the aforementioned iCPI-tree construction algorithm) are introduced and (3) all three algorithms are implemented on CUDA GPU platform and their performance is tested against an efficient multithreaded parallel implementation of iCPI-tree construction on CPU. Experiments prove that our solutions allow for large speedups over CPU version of the algorithm. This paper is an extension