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arXiv · 2407.05114

Approximating the Fr\'echet distance when only one curve is $c$-packed

Joachim Gudmundsson·Tiancheng Mai·Sampson Wong
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Abstract

One approach to studying the Fr\'echet distance is to consider curves that satisfy realistic assumptions. By now, the most popular realistic assumption for curves is $c$-packedness. Existing algorithms for computing the Fr\'echet distance between $c$-packed curves require both curves to be $c$-packed. In this paper, we only require one of the two curves to be $c$-packed. Our result is a nearly-linear time algorithm that $(1+\varepsilon)$-approximates the Fr\'echet distance between a $c$-packed curve and a general curve in $\mathbb R^d$, for constant values of $\varepsilon$, $d$ and $c$.

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Joachim Gudmundsson, Tiancheng Mai, Sampson Wong. 2024-07-06. Approximating the Fr\'echet distance when only one curve is $c$-packed. https://arxiv.org/abs/2407.05114

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