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Graphics processing units in acceleration of bandwidth selection for kernel density estimation

Andrzejewski W., Gramacki A., Gramacki J.

International Journal of Applied Mathematics and Computer Science

2013

Vol. 23, no. 4

869--885

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.

On line routing of guaranteed bandwidth with restoration

Olszewski I.

Electronics and Telecommunications Quarterly

2007

Vol. 53, No 1

23-38

In this paper the problem of finding a pair of link (node) disjoint active Label Switched Path (LSP) and backup LSP in Multi Protocol Label Switching (MPLS) networks is considered. It was assumed that capacity on the links of the backup Label Switched Paths can be shared. We focus on online algorithms for routing of guaranteed bandwidth of active LSPs and backup LSPs under partial information model in order to optimize the total amount of bandwidth consumed in the MPLS network. We consider only the case of protection against single link (node) failure. In this paper the comparison of two known routing algorithms was carried out. The first of them is based on Integer Linear Programming [3, 4] The second one is based on active-path-first heuristics [8]. In order to avoid the trap-problem the concept of Conflicting Link Set is used. Moreover, new algorithm based on active-path-first heuristics was proposed too. In this paper special attention has been paid to bandwidth consumed in the network, number of rejected connection set-up requests and running time of considered algorithms. The obtained results have proved that the proposed algorithm is comparable to the other algorithms but it has shorter running time then the existing ones.

O częstotliwości

Dobrogowski A.

Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne

1999

nr 4

197-202

Porównano częstotliwość widmową i chwilową. Wskazano na błędy, do których prowadziło nierozróżnienie pomiędzy tymi kategoriami częstotliwości. Podano podstawowe związki pomiędzy charakterystykami tych częstotliwości. Zwrócono uwagę, że istnieją sygnały, dla których jest możliwe lokalne utożsamienie częstotliwości chwilowej i widmowej. Uzupełniono objaśnienie mechanizmu dyskryminacji częstotliwości.

The spectral and instantaneous frequencies are compared. Some misinterpretations resulting from confusing these frequency categories are described. Important relations between some characteristics of the two frequencies are given. The local and global features of the instantaneous frequency are considered.