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arXiv · 1701.05909

Improving Sharir and Welzl's bound on crossing-free matchings through solving a stronger recurrence

Chenchao You
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Abstract

Sharir and Welzl [1] derived a bound on crossing-free matchings primarily based on solving a recurrence based on the size of the matchings. We show that the recurrence given in Lemma 2.3 in Sharir and Welzl can be improve to $(2n-6s)\textbf{Ma}_{m}(P)\leq\frac{68}{3}(s+2)\textbf{Ma}_{m-1}(P)$ and $(3n-7s)\textbf{Ma}_{m}(P)\leq44.5(s+2)\textbf{Ma}_{m-1}(P)$, thereby improving the upper bound for crossing-free matchings.

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Chenchao You. 2017-01-24. Improving Sharir and Welzl's bound on crossing-free matchings through solving a stronger recurrence. https://arxiv.org/abs/1701.05909

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