EunJungKim

Problems such as Vertex Cover and Multiway Cut have been well-studied in parameterized complexity. Cygan et al. 2011 drastically improved the running time of several problems including Multiway Cut and Almost 2SAT by employing LP-guided branching and aiming for FPT algorithms parameterized above LP lower bounds. Since then, LP-guided branching has been studied in depth …

Inspired by a width invariant defined on permutations by Guillemot and Marx , we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes, bounded rank-width graphs, map graphs, $K_t$-free unit $d$-dimensional ball graphs, posets with antichains of bounded size, and proper subclasses of dimension-2 posets all have bounded twin-width. On all these classes …

We present a new technique for designing fixed-parameter algorithms for graph cut problems in undirected graphs, which we call flow augmentation. Our technique is applicable to problems that can be phrased as a search for an (edge) $(s,t)$-cut of cardinality at most $k$ in an undirected graph $G$ with designated terminals s and t. …

The Weighted $\mathcal{F}$-Vertex Deletion for a class $\mathcal{F}$ of graphs asks, given a weighted graph $G$, for a minimum weight vertex set $S$ such that $G-S\in \mathcal{F}$. The case when $\mathcal{F}$ is minor-closed and excludes some graph as a minor has received particular attention but a constant-factor approximation remained elusive for Weighted $\mathcal …

We show a flow-augmentation algorithm in directed graphs: There exists a polynomial-time algorithm that, given a directed graph G, two integers $s,t\in V(G)$, and an integer $k$, adds (randomly) to $G$ a number of arcs such that for every minimal st-cut $Z$ in $G$ of size at most $k$, with probability $2^{-\mathrm{poly}(k)}$ the set $Z$ …