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.

In social network applications, individual opinion is often influenced by groups, and most decisions usually reflect the majority’s opinions. This imposes the group influence maximization (GIM) problem that selects $k$ initial nodes, where each node belongs to multiple groups for a given social network and each group has a weight, to maximize the weight of the eventually activated groups. The GIM problem is apparently NP-hard, given the NP-hardness of the influence maximization (IM) problem that does not consider groups. Focusing on activating groups rather than individuals, this paper proposes the complementary maximum coverage (CMC) algorithm, which greedily and iteratively removes the node with the approximate least group influence until at most $k$ nodes remain. Although the evaluation of the current group influence against each node is only approximate, it nevertheless ensures the success of activating an approximate maximum number of groups. Moreover, we also propose the improved reverse influence sampling (IRIS) algorithm through fine-tuning of the renowned reverse influence sampling algorithm for GIM. Finally, we carry out experiments to evaluate CMC and IRIS, demonstrating that they both outperform the baseline algorithms respective of their average number of activated groups under the independent cascade (IC) model.