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引用次数: 0
摘要
本文介绍了在三维矩形区域 [0, a] × [0, b] × [0, c] 实现 k 级覆盖所需的较小传感器数量 Nk(a,b,c)的一些理论结果。第一个特性概述了 Nk(a,b,c)数的一些理论结果,包括对称性、亚可加性和每个变量的单调性。然后,我们利用这些结果为 Nk(a,b,c)建立了一些下限和上限。我们的主要贡献是提出了一个关于实现 k 级覆盖的传感器最小密度的结果。
This paper presents some theoretical results on the smaller number Nk(a, b, c) of sensors to achieve k coverage for the 3D rectangular area [0, a] × [0, b] × [0, c]. The first properties outline some theoretical results for the numbers Nk(a, b, c), including symmetry, subadditivity, and monotony on each variable. We use then these results to establish some lower and upper bounds for Nk(a, b, c). The main contribution proposes a result concerning the minimal density of sensors to achieve k-coverage.