Coverage and hole-detection in sensor networks via homology

By Robert Ghrist, Abubakr Muhammad. IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005., 2005

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Boundary recognition in sensor networks by topological methods (2006, background): “[14] proposed an algorithm that detects holes via homology with no knowledge of sensor locations; however, the algorithm is centralized, with assumptions that both the sensing range and communication range are disks with radii carefully tuned.”
Random Walks on Simplicial Complexes and the normalized Hodge Laplacian (2018, background): “Simplicial complex models have been successful in developing new insights into biological data [32, 92], structural and functional connectivity in the brain [57,58,104], coverage of sensor networks [42,56,90,121], signal processing [8,115], mobility analysis [54], and robotics [105].”
Topological Data Analysis (2012, background): “The (weak) witness complex W is the clique complex of this (cid:15) -witness graph. is built on the gray landmark points, with the remaining black points acting as witnesses.”
On the Complexity of Neural Network Classifiers: A Comparison Between Shallow and Deep Architectures (2014, neutral): “The homology theory plays a fundamental role in many disciplines, including, for instance, physics [28], image processing [29], and sensor networks [30].”