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An efficient algorithm for identifying rainbow ortho-convex 4-sets in k-colored point sets (2404.06376v2)
Published 9 Apr 2024 in cs.CG and math.CO
Abstract: Let $P$ be a $k$-colored set of $n$ points in the plane, $4 \leq k \leq n$. We study the problem of deciding if $P$ contains a subset of four points of different colors such that its Rectilinear Convex Hull has positive area. We show this problem to be equivalent to deciding if there exists a point $c$ in the plane such that each of the open quadrants defined by $c$ contains a point of $P$, each of them having a different color. We provide an $O(n \log n)$-time algorithm for this problem, where the hidden constant does not depend on $k$; then, we prove that this problem has time complexity $\Omega(n \log n)$ in the algebraic computation tree model. No general position assumptions for $P$ are required.
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- David Flores-Peñaloza (8 papers)
- Mario A. Lopez (3 papers)
- Nestaly Marín (3 papers)
- David Orden (29 papers)