Related papers: Reconfiguration Using Generalized Token Jumping
In the m-\emph{Eternal Domination} game, a team of guard tokens initially occupies a dominating set on a graph $G$. An attacker then picks a vertex without a guard on it and attacks it. The guards defend against the attack: one of them has…
Robots with very limited capabilities are placed on the vertices of a graph and are required to move toward a single, common vertex, where they remain stationary once they arrive. This task is referred to as the GATHERING problem. Most of…
We study a variant of Set Cover where each element of the universe has some demand that determines how many times the element needs to be covered. Moreover, we examine two generalizations of this problem when a set can be included multiple…
A graph is reconstructible if it is determined up to isomorphism from the collection of all its one-vertex-deleted subgraphs, known as the deck of G. The Reconstruction Conjecture (RC) posits that every finite simple graph with at least…
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…
We study a family of sorting match puzzles on grids, which we call permutation match puzzles. In this puzzle, each row and column of a $n \times n$ grid is labeled with an ordering constraint -- ascending (A) or descending (D) -- and the…
We use the reconfiguration framework to analyze problems that involve the rearrangement of items among groups. In various applications, a group of items could correspond to the files or jobs assigned to a particular machine, and the goal of…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
In Two-Sets Cut-Uncut, we are given an undirected graph $G=(V,E)$ and two terminal sets $S$ and $T$. The task is to find a minimum cut $C$ in $G$ (if there is any) separating $S$ from $T$ under the following ``uncut'' condition. In the…
Image segmentation has come a long way since the early days of computer vision, and still remains a challenging task. Modern variations of the classical (purely bottom-up) approach, involve, e.g., some form of user assistance (interactive…
Given a network and a subset of interesting vertices whose identities are only partially known, the vertex nomination problem seeks to rank the remaining vertices in such a way that the interesting vertices are ranked at the top of the…
Current reconfiguration techniques are based on starting the system in a consistent configuration, in which all participating entities are in their initial state. Starting from that state, the system must preserve consistency as long as a…
Since Transformers are introduced into vision architectures, their quadratic complexity has always been a significant issue that many research efforts aim to address. A representative approach involves grouping tokens, performing…
In this letter we study the NP-complete vertex cover problem on finite connectivity random graphs. When the allowed size of the cover set is decreased, a discontinuous transition in solvability and typical-case complexity occurs. This…
A set $D$ of vertices in a graph $G$ is a dominating set if every vertex of $G$, which is not in $D$, has a neighbor in $D$. A set of vertices $D$ in $G$ is convex (respectively, isometric), if all vertices in all shortest paths…
We develop an approach called bounded combinatorial reconfiguration for solving combinatorial reconfiguration problems based on Answer Set Programming (ASP). The general task is to study the solution spaces of source combinatorial problems…
We study the Dominating set problem and Independent Set Problem for dynamic graphs in the vertex-arrival model. We say that a dynamic algorithm for one of these problems is $k$-stable when it makes at most $k$ changes to its output…
The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric…
We study problems of reconfiguration of shortest paths in graphs. We prove that the shortest reconfiguration sequence can be exponential in the size of the graph and that it is NP-hard to compute the shortest reconfiguration sequence even…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…