相关论文: Self-Reachable Chip Configurations on Trees

Given a connected, undirected, simple graph $G = (V, E)$ and $p \le |V|$ pebbles labeled $1,..., p$, a configuration of these $p$ pebbles is an injective map assigning the pebbles to vertices of $G$. Let $S$ and $D$ be two such…

Field Programmable Gate Arrays (FPGAs) have recently been increasingly used for highly-parallel processing of compute intensive tasks. This paper introduces an FPGA hardware platform architecture that is PC-based, allows for fast…

A graph $H$ is an \emph{isometric} subgraph of $G$ if $d_H(u,v)= d_G(u,v)$, for every pair~$u,v\in V(H)$. A graph is \emph{distance preserving} if it has an isometric subgraph of every possible order. A graph is \emph{sequentially distance…

The number of spanning trees in a graph $G$ is the total number of distinct spanning subgraphs of $G$ that are trees. In this paper we characterize the unique graph with a prescribed vertex (resp. edge) connectivity, minimum degree and…

This paper considers the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. The basic theory of herdable systems is…

Reconfigurable computing refers to the use of processors, such as Field Programmable Gate Arrays (FPGAs), that can be modified at the hardware level to take on different processing tasks. A reconfigurable computing platform describes the…

We discuss the amount of physical resources required to construct a given graph, where vertices are added sequentially. We naturally identify information -- distinct into instructions and memory -- and randomness as resources. Not…

Graphical chip-firing is a discrete dynamical system where chips are placed on the vertices of a graph and exchanged via simple firing moves. Recent work has sought to generalize chip-firing on graphs to higher dimensions, wherein graphs…

We investigate the decidability and complexity status of model-checking problems on unlabelled reachability graphs of Petri nets by considering first-order and modal languages without labels on transitions or atomic propositions on…

A set of fundamental matrices relating pairs of cameras in some configuration can be represented as edges of a "viewing graph". Whether or not these fundamental matrices are generically sufficient to recover the global camera configuration…

Behavior Trees are a task switching policy representation that can grant reactiveness and fault tolerance. Moreover, because of their structure and modularity, a variety of methods can be used to generate them automatically. In this short…

Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…

Given an ordered partition $\Pi =\{P_1,P_2, ...,P_t\}$ of the vertex set $V$ of a connected graph $G=(V,E)$, the \emph{partition representation} of a vertex $v\in V$ with respect to the partition $\Pi$ is the vector…

One of the most basic, longstanding open problems in the theory of dynamical systems is whether reachability is decidable for one-dimensional piecewise affine maps with two intervals. In this paper we prove that for injective maps, it is…

This paper presents new graph-theoretic conditions for structural target controllability of directed networks. After reviewing existing conditions and highlighting some gaps in the literature, we introduce a new class of network systems,…

In the \textsc{Coloring Reconfiguration} problem, we are given two proper $k$-colorings of a graph and asked to decide whether one can be transformed into the other by repeatedly applying a specified recoloring rule, while maintaining a…

A temporal graph is a graph whose edges appear at certain points in time. These graphs are temporally connected (in class TC) if all vertices can reach each other by temporal paths (traversing the edges in chronological order). Reachability…

Let T be an infinite homogenous tree of homogeneity $q+1$. Attaching to each edge the conductance $1$, the tree will became an electric network. The reversible Markov chain associated to this network is the simple random walk on the…

Many degree sequences can only be realised in graphs that contain a `ds-completable card', defined as a vertex-deleted subgraph in which the erstwhile neighbours of the deleted vertex can be identified from their degrees, if one knows the…

Reconfiguration schedules, i.e., sequences that gradually transform one solution of a problem to another while always maintaining feasibility, have been extensively studied. Most research has dealt with the decision problem of whether a…