arXiv subjects

Jaegun Lee

Publications and source records attributed to Jaegun Lee.

2 recordsLinked to original sources

arXiv2026

Bichromatic Line-Centers for Point Pairs

We study the \emph{bichromatic line-center problem} for $n$ pairs of points in the plane. A feasible solution assigns one point from each pair to the red set $R$ and the other to the blue set $B$. The goal is to minimize $\max\{w^\circ(R),\,w^\circ(B)\}$, where $w^\circ(X)$ denotes the minimum width of a strip enclosing $X$; the midlines of the corresponding optimal strips define the line-centers of $R$ and $B$. We consider several variants induced by orientational constraints on line-centers and provide efficient algorithms for each. For one line-center, which consists of computing a minimum-width strip that contains at least one point from each pair, we give an $O(n^2)$-time algorithm. For two line-centers, we obtain an $O(n)$-time algorithm when both are horizontal, and $Θ(n\log n)$-time algorithms when the two centers are parallel or when both orientations are prescribed. When exactly one orientation is prescribed, we give an $O(n^2)$-time algorithm. Finally, for the unrestricted case, we present an $O(n^3\log n)$-time algorithm.

cs.CG↗

arXiv2021

Rectangular Partitions of a Rectilinear Polygon

We investigate the problem of partitioning a rectilinear polygon $P$ with $n$ vertices and no holes % with no holes into rectangles using disjoint line segments drawn inside $P$ under two optimality criteria. In the minimum ink partition, the total length of the line segments drawn inside $P$ is minimized. We present an $O(n^3)$-time algorithm using $O(n^2)$ space that returns a minimum ink partition of $P$. In the thick partition, the minimum side length over all resulting rectangles is maximized. We present an $O(n^3 \log^2{n})$-time algorithm using $O(n^3)$ space that returns a thick partition using line segments incident to vertices of $P$, and an $O(n^6 \log^2{n})$-time algorithm using $O(n^6)$ space that returns a thick partition using line segments incident to the boundary of $P$. We also show that if the input rectilinear polygon has holes, the corresponding decision problem for the thick partition problem using line segments incident to vertices of the polygon is NP-complete. We also present an $O(m^3)$-time $3$-approximation algorithm for the minimum ink partition for a rectangle containing $m$ point holes.

cs.CG↗