In this paper,we propose a pioneering work on designing and programming B&B algorithms on GPU. To the best of our knowledge, no contribution has been proposed to raise such challenge. We focus on the parallel evaluation of the bounds for the Flow-shop scheduling problem. To deal with thread divergence caused by the bounding operation, we investigate two software based approaches called thread d...

In array processors, complex data reordering is often needed to realize the interconnection topologies between the computational nodes in algorithms. Several important algorithms, e.g., discrete trigonometric transforms and Viterbi decoding, can be represented in a radix-R form where the principal topology is stride by R permutation. In this paper, a general factorialization of stride permutati...

In this paper, conservative simultaneous confidence intervals for multiple comparisons among mean vectors in multivariate normal distributions are considered. Some properties of the multivariate Tukey-Kramer type procedures for pairwise comparisons and for comparisons with a control are presented. The upper bounds for the conservativeness of the procedures are discussed. Finally, numerical resu...

Depths are used to attempt to order the points of a multidimensional or infinite dimensional set from the “center of the set” to the “outer of it”. There are few definitions of depth which are valid in the functional case. One of them is the so-called random Tukey depth, which is based on some randomly chosen one-dimensional projections and thus varies (randomly) from computation to computation...

When performing a time series analysis of continuous data, for example from climate or environmental problems, the assumption that the process is Gaussian is often violated. Therefore, we introduce two non-Gaussian autoregressive time series models that are able to fit skewed and heavy-tailed time series data. Our two models are based on the Tukey g-and-h transformation. We discuss parameter es...

In animal toxicity studies, treatments are composed of a series of increasing doses including a vehicle control. The Tukey, Ciminera and Heyse (1985) trend test, referred to as Tukey’s trend test, is often performed to (1) test for linear trend in the response curve corresponding to three dose scales and possibly different dose ranges by deleting the higher doses, (2) identify the NOSTASOT (NO ...

Although there have been many compression schemes for reducing data effectively, most schemes do not consider the reordering of data. In the case of unordered data, if the users change the data order in a given data set, the compression ratio may be improved compared to the original compression before reordering data. However, in the case of ordered data, the users need a mapping table that map...

Random walk simulation is employed in many experimental algorithmic applications. Efficient execution on modern computer architectures demands that the random walk be implemented to exploit data locality for improving the cache performance. In this research, we demonstrate how different one-dimensional data reordering functionals can be used as a preprocessing step for speeding the random walk ...

Data reordering techniques are applied to improve the space and time efficiency of storage and query systems in various scientific and commercial applications. Run-length encoding is a prominent approach of compression in many areas, whose performance is significantly enhanced by achieving longer and fewer “runs” through data reordering. In this paper we theoretically study two reordering techn...