arXiv subjects

Chanho Song

Publications and source records attributed to Chanho Song.

2 recordsLinked to original sources

arXiv2026

Approximation Algorithm for the Min-Cost Bipartite Matching with Penalties

In this paper, we study the minimum-cost bipartite matching with penalties problem in metric spaces with bounded doubling dimension: Given two disjoint sets $R, B$ in a metric space $\mathcal{M}$ with $|R|+|B|=n$ and a penalty function $p \colon R \cup B \to \mathbb{R}_{\ge 0}$, the goal is to select a set of pairs in $R\times B$ so that every point belongs to at most one pair and the sum of the distances of the selected pairs and the penalties of the points not belonging to any pair is minimized. While near-linear time approximation algorithms are known for the minimum-cost perfect matching problem in geometric settings, no such algorithm was previously known for the penalty setting. We present a randomized algorithm that computes a $(1+\varepsilon)$-approximate minimum-cost bipartite matching with penalties in $O(n \mathrm{poly}(\log n, 1/\varepsilon))$ time with high probability. To the best of our knowledge, this is the first near-linear time approximation algorithm for the problem in the penalty setting.

cs.CG↗

arXiv2024

Dynamic parameterized problems on unit disk graphs

In this paper, we study fundamental parameterized problems such as $k$-Path/Cycle, Vertex Cover, Triangle Hitting Set, Feedback Vertex Set, and Cycle Packing for dynamic unit disk graphs. Given a vertex set $V$ changing dynamically under vertex insertions and deletions, our goal is to maintain data structures so that the aforementioned parameterized problems on the unit disk graph induced by $V$ can be solved efficiently. Although dynamic parameterized problems on general graphs have been studied extensively, no previous work focuses on unit disk graphs. In this paper, we present the first data structures for fundamental parameterized problems on dynamic unit disk graphs. More specifically, our data structure supports $2^{O(\sqrt{k})}$ update time and $O(k)$ query time for $k$-Path/Cycle. For the other problems, our data structures support $O(\log n)$ update time and $2^{O(\sqrt{k})}$ query time, where $k$ denotes the output size.

cs.DS↗