Eunjin Oh (오은진), 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 $i\in \{1,\dots ,k\}$. 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.