Improving Sharir and Welzl's bound on crossing-free matchings through solving a stronger recurrence
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)Mam(P)≤683(s+2)Mam-1(P) and (3n-7s)Mam(P)≤44.5(s+2)Mam-1(P), thereby improving the upper bound for crossing-free matchings.
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