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In this paper, we study the connectivity of a one-dimensional soft random geometric graph (RGG). The graph is generated by placing points at random on a bounded line segment and connecting pairs of points with a probability that depends on…
We present an algorithm for a fault tolerant Depth First Search (DFS) Tree in an undirected graph. This algorithm is drastically simpler than the current state-of-the-art algorithms for this problem, uses optimal space and optimal…
Rapidly-exploring Random Trees (RRTs) are a popular technique for autonomous exploration of mobile robots. However, the random sampling used by RRTs can result in inefficient and inaccurate frontiers extraction, which affects the…
The definition of $1$-planar graphs naturally extends graph planarity, namely a graph is $1$-planar if it can be drawn in the plane with at most one crossing per edge. Unfortunately, while testing graph planarity is solvable in linear time,…
Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph…
Delay and Disruption Tolerant Networks (DTNs) may lack continuous network connectivity. Routing in DTNs is thus a challenge since it must handle network partitioning, long delays, and dynamic topology. Meanwhile, routing protocols of the…
A common way to accelerate shortest path algorithms on graphs is the use of a bidirectional search, which simultaneously explores the graph from the start and the destination. It has been observed recently that this strategy performs…
Geographic routing is a routing paradigm, which uses geographic coordinates of network nodes to determine routes. Greedy routing, the simplest form of geographic routing forwards a packet to the closest neighbor towards the destination. A…
The Breadth First Search (BFS) algorithm is the foundation and building block of many higher graph-based operations such as spanning trees, shortest paths and betweenness centrality. The importance of this algorithm increases each day due…
Graph Neural Networks (GNNs) typically scale with the number of graph edges, making them well suited for sparse graphs but less efficient on dense graphs, such as point clouds or molecular interactions. A common remedy is to sparsify the…
Coverage motion planning is essential to a wide range of robotic tasks. Unlike conventional motion planning problems, which reason over temporal sequences of states, coverage motion planning requires reasoning over the spatial distribution…
For the problem of delivering a package from a source node to a destination node in a graph using a set of drones, we study the setting where the movements of each drone are restricted to a certain subgraph of the given graph. We consider…
Ensuring electricity grid reliability becomes increasingly challenging with the shift towards renewable energy and declining conventional capacities. Distribution System Operators (DSOs) aim to achieve grid reliability by verifying the n-1…
Occupancy grid maps (OGMs) are fundamental to most systems for autonomous robotic navigation. However, CPU-based implementations struggle to keep up with data rates from modern 3D lidar sensors, and provide little capacity for modern…
With geographic message dissemination, connected vehicles can be served with traffic information in their proximity, thereby positively impacting road safety, traffic management, or routing. Since such messages are typically relevant in a…
Graph Drawing techniques have been developed in the last few years with the purpose of producing aesthetically pleasing node-link layouts. Recently, the employment of differentiable loss functions has paved the road to the massive usage of…
Graph-based representations and message-passing modular policies constitute prominent approaches to tackling composable control problems in reinforcement learning (RL). However, as shown by recent graph deep learning literature, such local…
Provenance embedding algorithms are well known for tracking the footprints of information flow in wireless networks. Recently, low-latency provenance embedding algorithms have received traction in vehicular networks owing to strict…
Routing is a widespread approach to transfer information from a source node to a destination node in many deployed wireless ad-hoc networks. Today's implemented routing algorithms seek to efficiently find the path/route with the largest…
We propose a new frontier concept called the Gaussian Process Frontier (GP-Frontier) that can be used to locally navigate a robot towards a goal without building a map. The GP-Frontier is built on the uncertainty assessment of an efficient…