Submitted:
17 June 2026
Posted:
18 June 2026
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Abstract
We construct a k-shadow complex Δ_k(N) from the nerve N of a convex sensor cover. We prove that the region covered by at least k sensors is homotopy equivalent to Δ_k(N), recovering the usual nerve-based coverage test when k=1 and giving a direct combinatorial method for redundant coverage. A synthetic network computation for k=1,2 agrees with direct geometric sampling, and the scripts and data are supplied for reproduction.
Keywords:
sensor networks
; nerve complex
; k-fold coverage
; simplicial homology
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