Abstract. We show how to maintain the width of a set of n planar points subject to insertions and deletions of points in
$O(\sqrt{n}\log^3n)$
amortized time per update. Previously, no fully dynamic algorithm with a guaranteed sublinear time bound was known.
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Chan, . A Fully Dynamic Algorithm for Planar Width . Discrete Comput Geom 30, 17–24 (2003). https://doi.org/10.1007/s00454-003-2923-8
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DOI: https://doi.org/10.1007/s00454-003-2923-8