We investigate the problem of scheduling N jobs on parallel identical machines in J successive stages with finite buffer capacities between consecutive stages in a real-time environment. The objective is to find a schedule that minimizes the sum of weighted completion time of jobs. This problem has proven strongly NP-hard. In this paper, the scheduling problem is formulated as an integer programming model considering buffers as machines with zero processing time. Lagrangian relaxation algorithms are developed combined with a speed-up dynamic programming approach. The complication and time consumption of solving all the subproblems at each iteration in subgradient optimization motivate the development of the surrogate subgradient method, where only one subproblem is minimized at each iteration and an adaptive multiplier update scheme of Lagrangian multipliers is designed. Computational experiments with up to 100 jobs show that the designed surrogate subgradient algorithm provides a better performance as compared to the subgradient algorithm.

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The resource allocation for bag-of-tasks in the heterogeneous distributed system is to distribute the tasks to proper processors such that the makespan is minimized. It is a well-known NP-hard problem, and is even more complex and challenging when the processors have off-line time. To tackle this challenging problem, first, we set up a mathematical model for this problem which minimizes the makespan of the bag-oftasks with the off-line time segment of the processors. Second, to solve the model efficiently, we propose two new algorithms: a new scheduling algorithm referred to as sorting-allocation-pulling scheduling algorithm which first allocate the tasks to available time segment on proper processors and then pulls them to the formerly available time segment for the sake of minimizing the makespan, and an effective genetic algorithm with a novel local search operator and a well-designed modify operator. Finally, the numerical simulation experiments are conducted, and the two proposed algorithms are compared. The experimental results indicate the effectiveness of the proposed model and algorithms. INDEX TERMS Distributed computing, task scheduling, bag-of-tasks, generic algorithm.

Signcryption is a basic cryptographic primitive that simultaneously captures the functions of encryption and signature. To realize comprehensive information security against quantum computing attacks, lattice-based signcryption schemes have been successively proposed. However, the performance of signcryption schemes should be improved in the lattice setting. An efficient lattice-based signcryption scheme in the standard model is proposed in this paper. Under the ring learning with errors (RLWE) assumption and the ideal short integer solution (ISIS) assumption, the proposed signcryption scheme achieves indistinguishability against adaptive chosen ciphertext attacks (IND-CCA2) and existential unforgeability under an adaptive chosen-message attack (EUF-ACMA). Our scheme not only reduces the communication and computational overhead but also realizes a new design that combines the partitioning technique with the idea of tag-based key encapsulation. The performance analysis results show that our scheme is more efficient than previous lattice-based signcryption schemes in the standard model. INDEX TERMS Signcryption, lattice, encapsulation, ring learning with errors (RLWE) problem, ideal short integer solution (ISIS) problem.