Related papers: Navigable Graphs for High-Dimensional Nearest Neig…
Graph-based approaches to approximate nearest neighbor search (ANNS) enable fast, high-recall retrieval on billion-scale vector datasets. Among them, the Sparse Neighborhood Graph (SNG) is widely used due to its strong search performance.…
We establish tight lower and upper bounds on the number of edges in traceable graphs in several classes of dense graphs. A graph is traceable if it has a Hamiltonian path. We show that the bound is: - quadratic for the class of graphs of…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
Similarity graphs are an active research direction for the nearest neighbor search (NNS) problem. New algorithms for similarity graph construction are continuously being proposed and analyzed by both theoreticians and practitioners.…
Approximate nearest neighbor (ANN) search is a fundamental problem in many areas of data mining, machine learning and computer vision. The performance of traditional hierarchical structure (tree) based methods decreases as the…
Moving an autonomous agent through an unknown environment is one of the crucial problems for robotics and network analysis. Therefore, it received a lot of attention in the last decades and was analyzed in many different settings. The graph…
An identifying code of a graph is a dominating set which uniquely determines all the vertices by their neighborhood within the code. Whereas graphs with large minimum degree have small domination number, this is not the case for the…
Let $(X,\mathbf{d})$ be a metric space, $V\subseteq X$ a finite set, and $E \subseteq V \times V$. We call the graph $G(E,V)$ a {\em metric} graph if each edge $(u,v) \in E$ has weight $d(u,v)$. In particular edge $(u,u)$ is in the graph…
The classical problem of degree sequence realizability asks whether or not a given sequence of $n$ positive integers is equal to the degree sequence of some $n$-vertex undirected simple graph. While the realizability problem of degree…
Processing large complex networks recently attracted considerable interest. Complex graphs are useful in a wide range of applications from technological networks to biological systems like the human brain. Sometimes these networks are…
Navigability is a distinctive features of graphs associated with artificial or natural systems whose primary goal is the transportation of information or goods. We say that a graph $\mathcal{G}$ is navigable when an agent is able to…
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…
Random K-out graphs are used in several applications including modeling by sensor networks secured by the random pairwise key predistribution scheme, and payment channel networks. The random K-out graph with $n$ nodes is constructed as…
Neighbourly set of a graph is a subset of edges which either share an end point or are joined by an edge of that graph. The maximum cardinality neighbourly set problem is known to be NP-complete for general graphs. Mahdian (M.Mahdian, On…
Autonomous navigation is a key skill for assistive and service robots. To be successful, robots have to navigate avoiding going through the personal spaces of the people surrounding them. Complying with social rules such as not getting in…
A graph is called a $k$-planar unit distance graph if it can be drawn in the plane such that every edge is a unit line segment and is involved in at most $k$ crossings. We investigate $u_k(n)$, the maximum number of edges of such graphs on…
In this paper we introduce self-approaching graph drawings. A straight-line drawing of a graph is self-approaching if, for any origin vertex s and any destination vertex t, there is an st-path in the graph such that, for any point q on the…
A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…
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…
We study reachability and shortest paths problems in dynamic directed graphs. Whereas algebraic dynamic data structures supporting edge updates and reachability/distance queries have been known for quite a long time, they do not, in…