动态传感器网络覆盖的无坐标量化
Coordinate-Free Quantification of Coverage in Dynamic Sensor Networks
摘要：
我们提出了一套新的方法来分析动态传感器网络的覆盖特性。所考虑的动态传感器网络的研究通过一系列的快照，并表示为一系列的单纯形复合体，建立在每个时间点的通信图。一种来自计算拓扑学的方法称为zigzag persistent homology，它将这个单纯复形序列作为输入，并返回一个包含该序列中同源特征的出生和死亡时间的“条形码”。我们从这个输出中获得有用的统计数据，用于分析随时间变化的覆盖特性。此外，我们提出了一种方法，返回特定的代表性周期，这些同源的功能，在每一个点沿出生死亡的间隔。然后，这些代表性的周期被用于跟踪网络中的覆盖空洞，并获得每个时间点处的各个空洞的大小估计。一个加权的条形码，结合的大小信息，然后被用来作为一个视觉和定量的描述符的动态网络覆盖。
英文摘要：
We present a novel set of methods for analyzing coverage properties in dynamic sensor networks. The dynamic sensor network under consideration is studied through a series of snapshots, and is represented by a sequence of simplicial complexes, built from the communication graph at each time point. A method from computational topology called zigzag persistent homology takes this sequence of simplicial complexes as input, and returns a `barcode' containing the birth and death times of homological features in this sequence. We derive useful statistics from this output for analyzing time-varying coverage properties. Further, we propose a method which returns specific representative cycles for these homological features, at each point along the birth-death intervals. These representative cycles are then used to track coverage holes in the network, and obtain size estimates for individual holes at each time point. A weighted barcode, incorporating the size information, is then used as a visual and quantitative descriptor of the dynamic network coverage.
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