Related papers: Reconfiguring Multiple Connected Components with S…
We introduce a new framework for reconfiguration problems, and apply it to independent sets as the first example. Suppose that we are given an independent set $I_0$ of a graph $G$, and an integer $l \ge 0$ which represents a lower bound on…
Let $\mathcal{Q}$ be a vertex subset problem on graphs. In a reconfiguration variant of $\mathcal{Q}$ we are given a graph $G$ and two feasible solutions $S_s, S_t\subseteq V(G)$ of $\mathcal{Q}$ with $|S_s|=|S_t|=k$. The problem is to…
In the Vertex Cover Reconfiguration (VCR) problem, given a graph $G$, positive integers $k$ and $\ell$ and two vertex covers $S$ and $T$ of $G$ of size at most $k$, we determine whether $S$ can be transformed into $T$ by a sequence of at…
We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transformation, we consider…
The goal in {\em reconfiguration problems} is to compute a {\em gradual transformation} between two feasible solutions of a problem such that all intermediate solutions are also feasible. In the {\em Matching Reconfiguration Problem} (MRP),…
A vertex subset $I$ of a graph $G$ is called a $k$-path vertex cover if every path on $k$ vertices in $G$ contains at least one vertex from $I$. The \textsc{$k$-Path Vertex Cover Reconfiguration ($k$-PVCR)} problem asks if one can transform…
Coarse-Grain Reconfigurable Arrays (CGRAs) provide flexibility and energy efficiency in accelerating compute-intensive loops. Existing compilation techniques often struggle with scalability, unable to map code onto large CGRAs. To address…
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…
Suppose that we are given two independent sets I_b and I_r of a graph such that |I_b|=|I_r|, and imagine that a token is placed on each vertex in |I_b|. Then, the sliding token problem is to determine whether there exists a sequence of…
In a reconfiguration setting, each clique of a graph $G$ is viewed as a set of tokens placed on vertices of $G$ such that no vertex has more than one token and any two tokens are adjacent. Three well-known reconfiguration rules have been…
We settle the complexity of the Independent Set Reconfiguration problem on bipartite graphs under all three commonly studied reconfiguration models. We show that under the token jumping or token addition/removal model the problem is…
Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from…
Given a graph and two vertex sets satisfying a certain feasibility condition, a reconfiguration problem asks whether we can reach one vertex set from the other by repeating prescribed modification steps while maintaining feasibility. In…
The degree-constrained subgraph problem asks for a subgraph of a given graph such that the degree of each vertex is within some specified bounds. We study the following reconfiguration variant of this problem: Given two solutions to a…
Model-driven software engineering is a suitable method for dealing with the ever-increasing complexity of software development processes. Graphs and graph transformations have proven useful for representing such models and changes to them.…
A coloring of the vertices of a connected graph is convex if each color class induces a connected subgraph. We address the convex recoloring (CR) problem defined as follows. Given a graph $G$ and a coloring of its vertices, recolor a…
We study the problem of checking the existence of a step-by-step transformation of $d$-regular induced subgraphs in a graph, where $d \ge 0$ and each step in the transformation must follow a fixed reconfiguration rule. Our problem for $d=0$…
The Maximum Independent Set problem is fundamental for extracting conflict-free structure from large graphs, with applications in scheduling, recommendation, and network analysis. However, existing heuristics can stagnate when search…
We present the first results on the complexity of the reconfiguration of vertex separators under the three most popular rules: token addition/removal, token jumping, and token sliding. We show that, aside from some trivially negative…
We consider the computational complexity of reconfiguration problems, in which one is given two combinatorial configurations satisfying some constraints, and is asked to transform one into the other using elementary transformations, while…