2006/11/13 by V. de Silva, Robert Ghrist · 3 citations
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Homotopy and Cohomology in Algebraic Topology #Digital Image Processing Techniques #Robustness (evolution) #Topology (electrical circuits) #Probabilistic logic #Network topology #Computer science #Homology (biology) #Planar #Persistent homology #Distributed computing #Theoretical computer science #Formalism (music) #Algorithm #Mathematics #Mathematical optimization #Artificial intelligence #Computer network #Combinatorics
paper · doi:10.1177/0278364906072252
openalex publication_date 2006/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
Tools from computational homology are introduced to verify coverage in an idealized sensor network. These methods are unique in that, while they are coordinate-free and assume no localization or orientation capabilities for the nodes, there are also no probabilistic assumptions. The key ingredient is the theory of homology from algebraic topology. The robustness of these tools is demonstrated by adapting them to a variety of settings, including static planar coverage, 3-D barrier coverage, and time-dependent sweeping coverage. Results are also given on hole repair, error tolerance, optimal coverage, and variable radii. An overview of implementation is given.