Second-Order Analysis of Formation of Holes in Spatial Point Patterns: Applications in Wireless Sensor Networks

Dense deployment of wireless sensors can be used for environmental monitoring applications. Natural and artificial disasters, such as floods and fires, are significant events that need to be continuously monitored and contained as fast as possible. However, such disasters may destroy sensors deployed to monitor environmental conditions and prevent reporting of critical measurements that may indicate an occurring hazard. In this paper, we present how spatial point pattern analysis techniques, which have traditionally been used to analyze clustering, randomness, or regularity, can also be employed to analyze formation of a "hole" in a point pattern, which is also of significant interest in randomly deployed sensor networks since formation of a hole might be considered as an indication of a hazard. We first outline a methodology based on an information theoretic approach that can be used in decision support systems for detecting holes wherein visual inspection of destroyed sensors on a sensor map at a central station is hard, if not impossible. We show, by means of a second-order spatial point pattern analysis, that manifestation of such holes can be detected at small spatial scales. Furthermore, second-order analysis might provide an insight into the spatial scale of the hole in the pattern. Results presented validate our observations that failure of sensors due to a systematic destruction may be inferred by decision support systems when only a small portion of the monitored area is affected.