Grid peeling and the affine curve-shortening flow

יום א', 28/10/2018 - 14:00
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Experimentally, the convex-layer decomposition of subsets of the integer grid ("grid peeling") seems to behave at the limit like the affine curve-shortening flow. We offer some theoretical arguments to explain this phenomenon. In particular, we derive some rigorous results for the special case of peeling the quarter-infinite grid: We prove that, in this case, the number of grid points removed up to iteration n is Theta(n^(3/2)log n), and moreover, the boundary at iteration n is sandwiched between two hyperbolas that are separated from each other by a constant factor.

Joint work with David Eppstein and Sariel Har-Peled.