기초과학연구원 이산수학그룹
On March 7, 2023, Eunjin Oh (오은진) from POSTECH gave a talk at the Discrete Math Seminar on a new faster algorithm for solving the disjoint paths problem on planar graphs. The title of her talk was “Parameterized algorithms for the planar disjoint paths problem“.
Given an undirected planar graph $G$ with $n$ vertices and a set $T$ of $k$ pairs $(s_i,t_i)_{i=1}^k$ of vertices, the goal of the planar disjoint paths problem is to find a set $\mathcal P$ of $k$ pairwise vertex-disjoint paths connecting $s_i$ and $t_i$ for all indices $i\in\{1,\ldots,k\}$. This problem has been studied extensively due to its numerous applications such as VLSI layout and circuit routing. However, this problem is NP-complete even for grid graphs. This motivates the study of this problem from the viewpoint of parameterized algorithms.
In this talk, I will present a $2^{O(k^2)}n$-time algorithm for the planar disjoint paths problem. This improves the two previously best-known algorithms: $2^{2^{O(k)}}n$-time algorithm [Discrete Applied Mathematics 1995] and $2^{O(k^2)}n^6$-time algorithm [STOC 2020].
This is joint work with Kyungjin Cho and Seunghyeok Oh.
On October 5, 2021, Eunjin Oh (오은진) from POSTECH gave a talk at the Discrete Math Seminar on the parameterized complexity of the feedback vertex set problem on unit disk graphs at the Discrete Math Seminar. The title of her talk was “Feedback Vertex Set on Geometric Intersection Graphs“.
I am going to present an algorithm for computing a feedback vertex set of a unit disk graph of size k, if it exists, which runs in time $2^{O(\sqrt{k})}(n + m)$, where $n$ and $m$ denote the numbers of vertices and edges, respectively. This improves the $2^{O(\sqrt{k}\log k)}(n + m)$-time algorithm for this problem on unit disk graphs by Fomin et al. [ICALP 2017].