As data volume grows extensively, data profiling helps to extract metadata of large-scale data. However, one kind of metadata, order statistics, is difficult to be computed because they are not mergeable or incremental. Thus, the limitation of time and memory space does not support their computation on large-scale data. In this paper, we focus on an order statistic, quantiles, and present a comprehensive analysis of studies on approximate quantile computation. Both deterministic algorithms and randomized algorithms that compute approximate quantiles over streaming models or distributed models are covered. Then, multiple techniques for improving the efficiency and performance of approximate quantile algorithms in various scenarios, such as skewed data and high-speed data streams, are presented. Finally, we conclude with coverage of existing packages in different languages and with a brief discussion of the future direction in this area. INDEX TERMS Data profiling, order statistics, approximate quantile, streaming model, distributed model.
In this paper, based on probabilistic via-connection analysis of single vias and redundant vias, it is well known that on-track redundant via insertion is more important and critical than off-track redundant via insertion for yield optimization. Furthermore, a two-phase insertion approach for yield optimization is proposed to insert on-track redundant vias by finding a maximum matching result in a bipartite graph and insert off-track redundant vias by using a maximum constrained edge-pair matching result in a multi-partite graph with via-sharing constraints. According to the Poisson yield model for redundant via insertion, the experimental results show that our proposed two-phase insertion approach can increase 0.3%~7.4% wirelength to improve 4.3%~44.8% chip yield for the tested benchmarks.
Existing research on synthesis methods for single degree-of-freedom (DOF) six-bar linkages mainly include four or five exact poses. However, an ideal trajectory cannot be synthesized using only five exact poses, thus, it is necessary to introduce additional poses to constrain the trajectory. If more exact poses are introduced, then the linkage may have no solution. Therefore, the constraints of the approximate pose are considered to make the trajectory conform to the desired trajectory. This paper successfully introduces mixed poses into a six-bar linkage, based on Z (Z<5) exact poses and K approximate poses of a given error range, and a new synthesis method for single DOF six-bar linkages is proposed. The solution domain of the linkages synthesized by this method is wide and can be adjusted by controlling the error of the approximate poses, which reduces the difficulty of selecting the solution, ensures theoretical feasibility, and enables the trajectory of the final linkage to more closely match the ideal trajectory. Finally, for the coordinated training of multiple joints in human limbs, a rehabilitation device is designed based on the above six-bar linkage, and a prototype is developed and tested. The test results reveal the accuracy of the proposed method and the effectiveness of rehabilitation training.
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