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O-Joung Kwon

Publications and source records attributed to O-Joung Kwon.

3 recordsLinked to original sources
arXiv2021

A Unifying Framework for Characterizing and Computing Width Measures

Algorithms for computing or approximating optimal decompositions for decompositional parameters such as treewidth or clique-width have so far traditionally been tailored to specific width parameters. Moreover, for mim-width, no efficient algorithms for computing good decompositions were known, even under highly restrictive parameterizations. In this work we identify F-branchwidth as a class of generic decompositional parameters that can capture mim-width, treewidth, clique-width as well as other measures. We show that while there is an infinite number of F-branchwidth parameters, only a handful of these are asymptotically distinct. We then develop fixed-parameter and kernelization algorithms (under several structural parameterizations) that can compute every possible F-branchwidth, providing a unifying framework that can efficiently obtain near-optimal tree-decompositions, k-expressions, as well as optimal mim-width decompositions.

cs.DS↗
arXiv2021

A system of disjoint representatives of line segments with given $k$ directions

We prove that for all positive integers $n$ and $k$, there exists an integer $N = N(n,k)$ satisfying the following. If $U$ is a set of $k$ direction vectors in the plane and $\mathcal{J}_U$ is the set of all line segments in direction $u$ for some $u\in U$, then for every $N$ families $\mathcal{F}_1, \ldots, \mathcal{F}_N$, each consisting of $n$ mutually disjoint segments in $\mathcal{J}_U$, there is a set $\{A_1, \ldots, A_n\}$ of $n$ disjoint segments in $\bigcup_{1\leq i\leq N}\mathcal{F}_i$ and distinct integers $p_1, \ldots, p_n\in \{1, \ldots, N\}$ satisfying that $A_j\in \mathcal{F}_{p_j}$ for all $j\in \{1, \ldots, n\}$. We generalize this property for underlying lines on fixed $k$ directions to $k$ families of simple curves with certain conditions.

math.CO↗