With the development and widespread application of wireless sensor networks (WSNs), the amount of sensory data\ngrows sharply and the volumes of some sensory data sets are larger than terabytes, petabytes, or exabytes, which\nhave already exceeded the processing abilities of current WSNs. However, such big sensory data are not necessary for\nmost applications of WSNs, and only a small subset containing critical data points may be enough for analysis, where\nthe critical data points including the extremum and inflection data points of the monitored physical world during\ngiven period. Therefore, it is an efficient way to reduce the amount of the big sensory data set by only retrieving the\ncritical data points during sensory data acquisition process. Since most of the traditional sensory data acquisition\nalgorithms were only designed for discrete data and did not support to retrieve critical points from a continuously\nvarying physical world, this paper will study such a problem. In order to solve it, we firstly provided the formal\ndefinition of the �´-approximate critical points. Then, a data acquisition algorithm based on numerical analysis and\nLagrange interpolation is proposed to acquire the critical points. The extensive theoretical analysis and simulation\nresults are provided, which show that the proposed algorithm can achieve high accuracy for retrieving the\n�´-approximate critical points from the monitored physical world.
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