Two-stage submodular maximization problem under cardinality constraint has been widely studied in machine learning and combinatorial optimization. In this paper, we consider knapsack constraint. In this problem, we give $n$ articles and $m$ categories, and the goal is to select a subset of articles that can maximize the function $F(S)$. Function $F(S)$ consists of $m$ monotone submodular functions $f_j$, $j=1,2,\dots ,m$, and each $f_j$ measures the similarity of each article in category $j$. We present a constant-approximation algorithm for this problem.

With the prevalence of big-data technology, intricate, nanoscale Multi-Processor System-on-Chips (MP-SoCs) have been used in various safety-critical applications. However, with no extra countermeasures taken, this widespread use of MP-SoCs can lead to an undesirable decrease in their dependability. This study presents a promising approach using a group of Embedded Instruments (EIs) inside a processor core for health monitoring. Multiple health monitoring datasets obtained from the employed EIs are sampled and collated via the implemented experiment and thereafter used for conducting its remaining useful lifetime prognostics. This enables MP-SoCs to undertake preventive self-repair, thus realizing a zero mean downtime system and ensuring improved dependability. In addition, a principal component analysis based algorithm is designed for realizing the EI data fusion. Subsequently, a genetic algorithm based degradation optimization is employed to create a lifetime prediction model with respect to the processor.

Emerging applications widely use field-programmable gate array (FPGA) prototypes as a tool to verify modern very-large-scale integration (VLSI) circuits, imposing many problems, including routing failure caused by the limited number of connections among blocks of FPGAs therein. Such a shortage of connections can be alleviated through time-division multiplexing (TDM), by which multiple signals sharing an identical routing channel can be transmitted. In this context, the routing quality dominantly decides the performance of such systems, proposing the requirement of minimizing the signal delay between FPGA pairs. This paper proposes algorithms for the routing problem in a multi-FPGA system with TDM support, aiming to minimize the maximum TDM ratio. The algorithm consists of two major stages: (1) A method is proposed to set the weight of an edge according to how many times it is shared by the routing requirements and consequently to compute a set of approximate minimum Steiner trees. (2) A ratio assignment method based on the edge-demand framework is devised for assigning ratios to the edges respecting the TDM ratio constraints. Experiments were conducted against the public benchmarks to evaluate our proposed approach as compared with all published works, and the results manifest that our method achieves a better TDM ratio in comparison.