Accuracy of homology based approaches for coverage hole detection in wireless sensor networks

Homology theory provides new and powerful solutions to address the coverage problems in wireless sensor networks (WSNs). They are based on algebraic objects, such as Cech complex and Rips complex. Cech complex gives accurate information about coverage quality but requires a precise knowledge of the relative locations of nodes. This assumption is rather strong and hard to implement in practical deployments. Rips complex provides an approximation of Cech complex. It is easier to build and does not require knowledge of nodes location. This simplicity is at the expense of accuracy. Rips complex can not always detect all coverage holes. It is then necessary to evaluate its accuracy. This work proposes to use the area of undiscovered coverage holes per unit of surface as performance criteria. Investigations show that it depends on the ratio of communication and sensing ranges of each sensor. Closed form expressions for lower and upper bounds of the accuracy are also derived. Simulation results are consistent with the proposed analytical lower bound, with a maximum difference of 0.4%. Upper bound performance depends on the ratio of communication and sensing ranges.