Related papers: Parameterized Complexity of Critical Node Cuts
In this paper, we investigate three fundamental problems regarding cut complexes of graphs: their realizability, the uniqueness of graph reconstruction from them, and their algorithmic recognition. We define the parameter $m(d,n)$ as the…
Grid graphs, and, more generally, $k\times r$ grid graphs, form one of the most basic classes of geometric graphs. Over the past few decades, a large body of works studied the (in)tractability of various computational problems on grid…
We consider a the minimum k-way cut problem for unweighted graphs with a size bound s on the number of cut edges allowed. Thus we seek to remove as few edges as possible so as to split a graph into k components, or report that this requires…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
Given a directed graph $G$, a set of $k$ terminals and an integer $p$, the \textsc{Directed Vertex Multiway Cut} problem asks if there is a set $S$ of at most $p$ (nonterminal) vertices whose removal disconnects each terminal from all other…
We show that the following two problems are fixed-parameter tractable with parameter k: testing whether a connected n-vertex graph with m edges has a square root with at most n-1+k edges and testing whether such a graph has a square root…
Fully dynamic graph is a data structure that (1) supports edge insertions and deletions and (2) answers problem specific queries. The time complexity of (1) and (2) are referred to as the update time and the query time respectively. There…
When considering a graph problem from a parameterized point of view, the parameter chosen is often the size of an optimal solution of this problem (the "standard" parameter). A natural subject for investigation is what happens when we…
In the Hedge Cut problem, the edges of a graph are partitioned into groups called hedges, and the question is what is the minimum number of hedges to delete to disconnect the graph. Ghaffari, Karger, and Panigrahi [SODA 2017] showed that…
In this work, we initiate a thorough study of parameterized graph optimization problems in the distributed setting. In a parameterized problem, an algorithm decides whether a solution of size bounded by a \emph{parameter} $k$ exists and if…
We present the first results on the parameterized complexity of reconfiguration problems, where a reconfiguration version of an optimization problem $Q$ takes as input two feasible solutions $S$ and $T$ and determines if there is a sequence…
The Steiner Multicut problem asks, given an undirected graph G, terminals sets T1,...,Tt $\subseteq$ V(G) of size at most p, and an integer k, whether there is a set S of at most k edges or nodes s.t. of each set Ti at least one pair of…
The Independent Cutset problem asks whether there is a set of vertices in a given graph that is both independent and a cutset. Such a problem is $\textsf{NP}$-complete even when the input graph is planar and has maximum degree five. In this…
A graph is $c$-closed when every pair of nonadjacent vertices has at most $c-1$ common neighbors. In $c$-Closed Vertex Deletion, the input is a graph $G$ and an integer $k$ and we ask whether $G$ can be transformed into a $c$-closed graph…
In this paper we study the problem of finding a small safe set $S$ in a graph $G$, i.e. a non-empty set of vertices such that no connected component of $G[S]$ is adjacent to a larger component in $G - S$. We enhance our understanding of the…
The study of parameterized streaming complexity on graph problems was initiated by Fafianie et al. (MFCS'14) and Chitnis et al. (SODA'15 and SODA'16). Simply put, the main goal is to design streaming algorithms for parameterized problems…
Given a bipartite graph $G$, the \textsc{Bicluster Editing} problem asks for the minimum number of edges to insert or delete in $G$ so that every connected component is a bicluster, i.e. a complete bipartite graph. This has several…
Detecting critical nodes in sparse graphs is important in a variety of application domains, such as network vulnerability assessment, epidemic control, and drug design. The critical node problem (CNP) aims to find a set of critical nodes…
We study the fixed-parameter tractability of the following fundamental problem: given two directed graphs $\vec H$ and $\vec G$, count the number of copies of $\vec H$ in $\vec G$. The standard setting, where the tractability is well…
We study deterministic algorithms for computing graph cuts, with focus on two fundamental problems: balanced sparse cut and $k$-vertex connectivity for small $k$ ($k=O(\polylog n)$). Both problems can be solved in near-linear time with…