Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times - a polymatroid optimization approach

We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem. We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can be solved in $ \O({\rm T}_{\rm feas}(n) \times\log n)$ time by using our divide-and-conquer technique, where n is the number of jobs and Tfeas(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper.

A fast, streaming SIMD extensions 2, logistic squashing function

Schraudolph proposed an excellent exponential approximation providing increased performance particularly suited to the logistic squashing function used within many neural networking applications. This note applies Intel's streaming SIMD Extensions 2 (SSE2), where SIMD is single instruction multiple data, of the Pentum IV class processor to Schraudolph's technique, further increasing the performance of the logistic squashing function. It was found that the calculation of the new 32-bit SSE2 logistic squashing function described here was up to 38 times faster than the conventional exponential function and up to 16 times faster than a Schraudolph-style 32-bit method on an Intel Pentum D 3.6 GHz CPU.

Artificial neural networks in modelling osmotic dehydration of foods

Artificial neural network (ANN) models for water loss (WL) and solid gain (SG) were evaluated as potential alternative to multiple linear regression (MLR) for osmotic dehydration of apple, banana and potato. The radial basis function (RBF) network with a Gaussian function was used in this study. The RBF employed the orthogonal least square learning method. When predictions of experimental data from MLR and ANN were compared, an agreement was found for ANN models than MLR models for SG than WL. The regression coefficient for determination (R2) for SG in MLR models was 0.31, and for ANN was 0.91. The R2 in MLR for WL was 0.89, whereas ANN was 0.84.Osmotic dehydration experiments found that the amount of WL and SG occurred in the following descending order: Golden Delicious apple > Cox apple > potato > banana. The effect of temperature and concentration of osmotic solution on WL and SG of the plant materials followed a descending order as: 55 > 40 > 32.2C and 70 > 60 > 50 > 40%, respectively.