Multitasking Scheduling with Shared Processing

Recently, the problem of multitasking scheduling has attracted a lot of attention in the service industries where workers frequently perform multiple tasks by switching from one task to another. Hall, Leung and Li (Discrete Applied Mathematics 2016) proposed a shared processing multitasking scheduling model which allows a team to continue to work on the primary tasks while processing the routinely scheduled activities as they occur. The processing sharing is achieved by allocating a fraction of the processing capacity to routine jobs and the remaining fraction, which we denote as sharing ratio, to the primary jobs. In this paper, we generalize this model to parallel machines and allow the fraction of the processing capacity assigned to routine jobs to vary from one to another. The objectives are minimizing makespan and minimizing the total completion time. We show that for both objectives, there is no polynomial time approximation algorithm unless P=NP if the sharing ratios are arbitrary for all machines. Then we consider the problems where the sharing ratios on some machines have a constant lower bound. For each objective, we analyze the performance of the classical scheduling algorithms and their variations and then develop a polynomial time approximation scheme when the number of machines is a constant

Sublinear Approximation Schemes for Scheduling Precedence Graphs of Bounded Depth

We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth h. Our goal is to minimize the maximum completion time. We focus on developing approximation algorithms that use only sublinear space or sublinear time. We develop the first one-pass streaming approximation schemes using sublinear space when all jobs\u27 processing times differ no more than a constant factor c and the number of machines m is at most 2nϵ3hc. This is so far the best approximation we can have in terms of m, since no polynomial time approximation better than 43 exists when m=n3 unless P=NP. %the problem cannot be approximated within a factor of 43 when m=n3 even if all jobs have equal processing time. The algorithms are then extended to the more general problem where the largest αn jobs have no more than c factor difference. % for some constant

Streaming Approximation Scheme for Minimizing Total Completion Time on Parallel Machines Subject to Varying Processing Capacity

We study the problem of minimizing total completion time on parallel machines subject to varying processing capacity. In this paper, we develop an approximation scheme for the problem under the data stream model where the input data is massive and cannot fit into memory and thus can only be scanned for a few passes. Our algorithm can compute the approximate value of the optimal total completion time in one pass and output the schedule with the approximate value in two passes

Streaming Approximation Scheme for Minimizing Total Completion Time on Parallel Machines Subject to Varying Processing Capacity

We study the problem of minimizing total completion time on parallel machines subject to varying processing capacity. In this paper, we develop an approximation scheme for the problem under the data stream model where the input data is massive and cannot fit into memory and thus can only be scanned for a few passes. Our algorithm can compute the approximate value of the optimal total completion time in one pass and output the schedule with the approximate value in two passes

Streaming algorithms for multitasking scheduling with shared processing

In this paper, we design the first streaming algorithms for the problem of multitasking scheduling on parallel machines with shared processing. In one pass, our streaming approximation schemes can provide an approximate value of the optimal makespan. If the jobs can be read in two passes, the algorithm can find the schedule with the approximate value. This work not only provides an algorithmic big data solution for the studied problem, but also gives an insight into the design of streaming algorithms for other problems in the area of scheduling

Streaming Algorithms for Multitasking Scheduling with Shared Processing

In this paper, we design the first streaming algorithms for the problem of multitasking scheduling on parallel machines with shared processing. In one pass, our streaming approximation schemes can provide an approximate value of the optimal makespan. If the jobs can be read in two passes, the algorithm can find the schedule with the approximate value. This work not only provides an algorithmic big data solution for the studied problem, but also gives an insight into the design of streaming algorithms for other problems in the area of scheduling

Multitasking Scheduling with Shared Processing

Recently, the problem of multitasking scheduling has attracted a lot of attention in the service industries where workers frequently perform multiple tasks by switching from one task to another. Hall, Leung and Li (Discrete Applied Mathematics 2016) proposed a shared processing multitasking scheduling model which allows a team to continue to work on the primary tasks while processing the routinely scheduled activities as they occur. The processing sharing is achieved by allocating a fraction of the processing capacity to routine jobs and the remaining fraction, which we denote as sharing ratio, to the primary jobs. In this paper, we generalize this model to parallel machines and allow the fraction of the processing capacity assigned to routine jobs to vary from one to another. The objectives are minimizing makespan and minimizing the total completion time. We show that for both objectives, there is no polynomial time approximation algorithm unless P = NP if the sharing ratios are arbitrary for all machines. Then we consider the problems where the sharing ratios on some machines have a constant lower bound. For each objective, we analyze the performance of the classical scheduling algorithms and their variations and then develop a polynomial time approximation scheme when the number of machines is a constant

Metal adsorption by quasi cellulose xanthogenates derived from aquatic and terrestrial plant materials

The FTIR spectra, SEM-EDXA and copper adsorption capacities of the raw plant materials, alkali treated straws and cellulose xanthogenate derivatives of Eichhornia crassipes shoot, rape straw and corn stalk were investigated. FTIR spectra indicated that of the three plant materials, the aquatic biomass of Eichhornia crassipes shoot contained more O-H and C=O groups which accounted for the higher Cu²⁺ adsorption capacities of the raw and alkali treated plant material. SEM-EDXA indicated the incorporation of sulphur and magnesium in the cellulose xanthogenate. The Cu²⁺ adsorption capacities of the xanthogenates increased with their magnesium and sulphur contents. However more copper was adsorbed than that can be explained by exchange of copper with magnesium. Precipitation may contribute to the enhanced uptake of copper by the cellulose xanthogenate

Relativistic Kinematics Without Numerical Cancellation

Computer Science

PREDICTING METHOD OF NATURAL FREQUENCY FOR SHIP’S OVERALL VERTICAL VIBRATION

At ship design stage, empirical formulas are generally used to predict the overall vertical vibration natural frequency of ship to avoid the harmful resonance against main excitation. Nowadays, with the development of modern large-scale ships, the existing empirical formulas are becoming unpractical, some corrections shall be applied on these classical formulas or a new formula is to be derived for the prediction of vertical vibration frequencies of ship. In this paper, a new empirical formula is given for predicting the natural frequency of ship overall vertical vibration. Based on the Timoshenko beam theory, the formula is derived by introducing by shear coefficient to correction shear uniform distribution hypothesis for a thin-walled box beam with free-free boundary condition. This new formula is obtained by statistical analysis for large amounts of measured natural frequency results of the ship overall vertical vibration. The proposed prediction method in this paper was used to predict the natural frequencies of six ships. The predicted natural frequencies are consistent with that by measurements. The comparison with measurements show that the formula proposed in this article is more feasible to use, and also provide a new method to the prediction of natural frequency of the ship overall vertical vibration