Related papers: Succinct Greedy Geometric Routing in the Euclidean…
We present PIE, a scalable routing scheme that achieves 100% packet delivery and low path stretch. It is easy to implement in a distributed fashion and works well when costs are associated to links. Scalability is achieved by using virtual…
The greedy spanner is a high-quality spanner: its total weight, edge count and maximal degree are asymptotically optimal and in practice significantly better than for any other spanner with reasonable construction time. Unfortunately, all…
In this paper, we design a greedy routing on networks of mobile agents. In the greedy routing algorithm, every time step a packet in agent $i$ is delivered to the agent $j$ whose distance from the destination is shortest among searched…
Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…
A graph is called (generically) rigid in $\mathbb{R}^d$ if, for any choice of sufficiently generic edge lengths, it can be embedded in $\mathbb{R}^d$ in a finite number of distinct ways, modulo rigid transformations. Here we deal with the…
We address the problem of efficient and unobstructed surveillance or communication in complex environments. On one hand, one wishes to use a minimal number of sensors to cover the environment. On the other hand, it is often important to…
In this paper we study local routing strategies on geometric graphs. Such strategies use geometric properties of the graph like the coordinates of the current and target nodes to route. Specifically, we study routing strategies in the…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
The enormous amount of data to be represented using large graphs exceeds in some cases the resources of a conventional computer. Edges in particular can take up a considerable amount of memory as compared to the number of nodes. However,…
Bidirectional motion planning often reduces planning time compared to its unidirectional counterparts. It requires connecting the forward and reverse search trees to form a continuous path. However, this process could fail and restart the…
In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general…
A greedy omnidirectional relay scheme is developed, and the corresponding achievable rate region is obtained for the all-source all-cast problem. The discussions are first based on the general discrete memoryless channel model, and then…
Telemetry-Aware routing promises to increase efficacy and responsiveness to traffic surges in computer networks. Recent research leverages Machine Learning to deal with the complex dependency between network state and routing, but…
The fundamental idea of embedding a network in a metric space is rooted in the principle of proximity preservation. Nodes are mapped into points of the space with pairwise distance that reflects their proximity in the network. Popular…
Let $V\subset\mathbb{R}^2$ be a set of $n$ sites in the plane. The unit disk graph $DG(V)$ of $V$ is the graph with vertex set $V$ in which two sites $v$ and $w$ are adjacent if and only if their Euclidean distance is at most $1$. We…
In this paper, we provide an algorithm for traversing geometric graphs which visits all vertices, and reports every vertex and edge exactly once. To achieve this, we combine a given geometric graph $G$ with the integer lattice, seen as a…
We consider a swarm of $n$ autonomous mobile robots, distributed on a 2-dimensional grid. A basic task for such a swarm is the gathering process: All robots have to gather at one (not predefined) place. A common local model for extremely…
Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…
Geometric routing algorithms like GFG (GPSR) are lightweight, scalable algorithms that can be used to route in resource-constrained ad hoc wireless networks. However, such algorithms run on planar graphs only. To efficiently construct a…
A communication network is a graph in which each node has only local information about the graph and nodes communicate by passing messages along its edges. Here, we consider the {\it geometric communication network} where the nodes also…