Related papers: Using Binoculars for Fast Exploration and Map Cons…
This work addresses the challenge of patrolling regular grid graphs of any dimension using a single mobile agent with minimal memory and limited sensing range. We show that it is impossible to patrol some grid graphs with $0$ bits of…
The graph exploration problem is to visit all the nodes of a connected graph by a mobile entity, e.g., a robot. The robot has no a priori knowledge of the topology of the graph or of its size. Cohen et al. \cite{Ilcinkas08} introduced label…
We study the problem of treasure hunt in a graph by a mobile agent. The nodes in the graph are anonymous and the edges at any node $v$ of degree $deg(v)$ are labeled arbitrarily as $0,1,\ldots, deg(v)-1$. A mobile agent, starting from a…
We give lower bounds for various natural node- and edge-based local strategies for exploring a graph. We consider this problem both in the setting of an arbitrary graph as well as the abstraction of a geometric exploration of a space by a…
In this paper, we use the theory of Riordan matrices to introduce the notion of a Riordan graph. The Riordan graphs are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other…
We study the Temporal Exploration problem, where an agent must visit all vertices of a temporal graph while traversing at most one available edge per time step. Unlike static graphs, which can be explored in linear time, temporal…
We study the exploration problem by mobile agents in two prominent models of dynamic graphs: $1$-Interval Connectivity and Connectivity Time. The $1$-Interval Connectivity model was introduced by Kuhn et al.~[STOC 2010], and the…
Triangle counting in a graph is a fundamental problem with wide-ranging applications. It is crucial for understanding graph structure and serves as a basis for more advanced graph analytics. One key application is truss decomposition, a…
Random walks by single-node agents have been systematically conducted on various types of complex networks in order to investigate how their topologies can affect the dynamics of the agents. However, by fitting any network node, these…
Chordal graphs can be used to encode dependency models that are representable by both directed acyclic and undirected graphs. This paper discusses a very simple and efficient algorithm to learn the chordal structure of a probabilistic model…
Understanding the geometric relationships between objects in a scene is a core capability in enabling both humans and autonomous agents to navigate in new environments. A sparse, unified representation of the scene topology will allow…
In this paper we present the first algorithm in the streaming model to characterize completely the biconnectivity properties of undirected networks: articulation points, bridges, and connected and biconnected components. The motivation of…
Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…
We study a very restrictive graph exploration problem. In our model, an agent without persistent memory is placed on a vertex of a graph and only sees the adjacent vertices. The goal is to visit every vertex of the graph, return to the…
\emph{Temporal graphs} are a generalisation of (static) graphs, defined by a sequence of \emph{snapshots}, each a static graph defined over a common set of vertices. \emph{Exploration} problems are one of the most fundamental and most…
Temporal graphs are a class of graphs defined by a constant set of vertices and a changing set of edges, each of which is known as a timestep. These graphs are well motivated in modelling real-world networks, where connections may change…
As more and more network-structured data sets are available, the statistical analysis of valued graphs has become common place. Looking for a latent structure is one of the many strategies used to better understand the behavior of a…
We consider monotonicity problems for graph searching games. Variants of these games - defined by the type of moves allowed for the players - have been found to be closely connected to graph decompositions and associated width measures such…
Minimum Spanning Tree (MST) and Breadth-First Search (BFS) tree constructions are classical problems in distributed computing, traditionally studied in the message-passing model, where static nodes communicate via messages. This paper…
One or more searchers must capture an invisible evader hiding in the nodes of a graph. We study this graph search problem; we emphasize that we study the capture of a node-located evader, which has received less attention than edge search.…