Related papers: How to Reconfigure Your Alliances

In a graph, a vertex dominates itself and its neighbors, and a dominating set is a set of vertices that together dominate the entire graph. Given a graph and two dominating sets of equal size $k$, the {\em Dominating Set Reconfiguration…

Reconfiguration problems ask whether one feasible solution can be transformed into another by a sequence of local moves while maintaining feasibility throughout. For integers $d \geq 1$ and $k \geq d+1$, the Distance Coloring problem asks…

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 study {\sc Cluster Edge Modification} problems with constraints on the size of the clusters. A graph $G$ is a cluster graph if every connected component of $G$ is a clique. In a typical {\sc Cluster Edge Modification} problem such as the…

We study the problem of deciding reconfigurability of target sets of a graph. Given a graph $G$ with vertex thresholds $\tau$, consider a dynamic process in which vertex $v$ becomes activated once at least $\tau(v)$ of its neighbors are…

The reconfiguration problem for homomorphisms of digraphs to a reflexive digraph cycle, which amounts to deciding if a `reconfiguration graph' is connected, is known to by polynomially time solvable via a greedy algorithm based on certain…

Suppose that we are given two dominating sets $D_s$ and $D_t$ of a graph $G$ whose cardinalities are at most a given threshold $k$. Then, we are asked whether there exists a sequence of dominating sets of $G$ between $D_s$ and $D_t$ such…

Network alignment, or the task of finding meaningful node correspondences between nodes in different graphs, is an important graph mining task with many scientific and industrial applications. An important principle for network alignment is…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets of an interval or a permutation graph. In these problems, one asks to find a subset of vertices, normally called a…

Our work is motivated by the challenges presented in preparing arrays of atoms for use in quantum simulation. The recently-developed process of loading atoms into traps results in approximately half of the traps being filled. To consolidate…

Given a graph $G$ and two independent sets of $G$, the independent set reconfiguration problem asks whether one independent set can be transformed into the other by moving a single vertex at a time, such that at each intermediate step we…

Reconfiguration is one of the central mechanisms in distributed systems. Due to failures and connectivity disruptions, the very set of service replicas (or servers) and their roles in the computation may have to be reconfigured over time.…

The Offensive Alliance problem has been studied extensively during the last twenty years. A set $S\subseteq V$ of vertices is an offensive alliance in an undirected graph $G=(V,E)$ if each $v\in N(S)$ has at least as many neighbours in $S$…

We continue the study of token sliding reconfiguration graphs of independent sets initiated by the authors in an earlier paper (arXiv:2203.16861). Two of the topics in that paper were to study which graphs $G$ are token sliding graphs and…

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…

A vertex-subset graph problem $Q$ defines which subsets of the vertices of an input graph are feasible solutions. The reconfiguration version of a vertex-subset problem $Q$ asks whether it is possible to transform one feasible solution for…

Spatial co-location pattern mining refers to the task of discovering the group of objects or events that co-occur at many places. Extracting these patterns from spatial data is very difficult due to the complexity of spatial data types,…

Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…

Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…