Optimal conditions for connectedness of discretized sets

Boris Brimkov () and Valentin E. Brimkov ()
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Boris Brimkov: Slippery Rock University
Valentin E. Brimkov: SUNY Buffalo State

Journal of Combinatorial Optimization, 2022, vol. 43, issue 5, No 26, 1493-1506

Abstract: Abstract An offset discretization of a set $$X \subset {\mathbb {R}}^n$$ X ⊂ R n is obtained by taking the integer points inside a closed neighborhood of X of a certain radius. In this work we determine a minimum threshold for the offset radius, beyond which the discretization of an arbitrary (possibly disconnected) set is always connected. The obtained results hold for a broad class of disconnected subsets of $${\mathbb {R}}^n$$ R n and generalize several previous results. We also extend our results to infinite discretizations of unbounded subsets of $${\mathbb {R}}^n$$ R n and consider certain algorithmic aspects. The obtained results can be applied to component topology preservation as well as extracting geometric features and connectivity control of very large object discretizations.

Keywords: Discrete geometry; Geometric features; Connected set; Discrete connectivity; Connectivity control; Offset discretization (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-020-00691-0

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