Related papers: How to Reconfigure Your Alliances
We introduce in a general setting a dynamic programming method for solving reconfiguration problems. Our method is based on contracted solution graphs, which are obtained from solution graphs by performing an appropriate series of edge…
Imagine that unlabelled tokens are placed on the edges of a graph, such that no two tokens are placed on incident edges. A token can jump to another edge if the edges having tokens remain independent. We study the problem of determining the…
In a reconfiguration problem, we are given two feasible solutions of a combinatorial problem and our goal is to determine whether it is possible to reconfigure one into the other, with the steps dictated by specific reconfiguration rules.…
Let $S$ be an independent set of a simple undirected graph $G$. Suppose that each vertex of $S$ has a token placed on it. The tokens are allowed to be moved, one at a time, by sliding along the edges of $G$, so that after each move, the…
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 $S$ as it has neighbours (including itself) not in $S$. We study the classical and…
Coordinating the motion of multiple agents in constrained environments is a fundamental challenge in robotics, motion planning, and scheduling. A motivating example involves $n$ robotic arms, each represented as a line segment. The…
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…
\textsc{Directed Token Sliding} asks, given a directed graph and two sets of pairwise nonadjacent vertices, whether one can reach from one set to the other by repeatedly applying a local operation that exchanges a vertex in the current set…
In this paper, we show that several graph parameters are known in different areas under completely different names. More specifically, our observations connect signed domination, monopolies, $\alpha$-domination, $\alpha$-independence,…
Reconfiguration problems involve determining whether two given configurations can be transformed into each other under specific rules. The Token Sliding problem asks whether, given two different set of tokens on vertices of a graph $G$, we…
With distributed computing and mobile applications becoming ever more prevalent, synchronizing diverging replicas of the same data is a common problem. Reconciliation -- bringing two replicas of the same data structure as close as possible…
We consider the following problem for a fixed graph H: given a graph G and two H-colorings of G, i.e. homomorphisms from G to H, can one be transformed (reconfigured) into the other by changing one color at a time, maintaining an H-coloring…
Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…
We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of…
The analysis of (social) networks and multi-agent systems is a central theme in Artificial Intelligence. Some line of research deals with finding groups of agents that could work together to achieve a certain goal. To this end, different…
We introduce a new model of indeterminacy in graphs: instead of specifying all the edges of the graph, the input contains all triples of vertices that form a connected subgraph. In general, different (labelled) graphs may have the same set…
Graphs are a powerful mathematical model, and they are used to represent real-world structures in various fields. In many applications, real-world structures with high connectivity and robustness are preferable. For enhancing the…
We study the problem of reconfiguring odd matchings, that is, matchings that cover all but a single vertex. Our reconfiguration operation is a so-called flip where the unmatched vertex of the first matching gets matched, while consequently…
Solving task planning problems involving multiple objects and multiple robotic arms poses scalability challenges. Such problems involve not only coordinating multiple high-DoF arms, but also searching through possible sequences of actions…
A set $D$ of vertices of a graph is a \emph{defensive alliance} if, for each element of $D$, the majority of its neighbours are in $D$. We consider the notion of local minimality in this paper. We are interested in finding a locally minimal…