Related papers: Edge N-Level Sparse Visibility Graphs: Fast Optima…
Given an n-vertex graph G, a drawing of G in the plane is a mapping of its vertices into points of the plane, and its edges into continuous curves, connecting the images of their endpoints. A crossing in such a drawing is a point where two…
Current point-based approaches encounter limitations in scalability and rendering quality when using large 3D point cloud maps because using them directly for novel view synthesis (NVS) leads to degraded visualizations. We identify the…
The graph-navigability problem concerns how one can find as short paths as possible between a pair of vertices, given an incomplete picture of a graph. We study the navigability of graphs where the vertices are tagged by a number (between 1…
We present new quantum algorithms for Triangle Finding improving its best previously known quantum query complexities for both dense and spare instances.For dense graphs on $n$ vertices, we get a query complexity of $O(n^{5/4})$ without any…
The problem of sparsifying a graph or a hypergraph while approximately preserving its cut structure has been extensively studied and has many applications. In a seminal work, Bencz\'ur and Karger (1996) showed that given any $n$-vertex…
We consider the problem of designing succinct data structures for interval graphs with $n$ vertices while supporting degree, adjacency, neighborhood and shortest path queries in optimal time in the $\Theta(\log n)$-bit word RAM model. The…
The absence of the efficient methods for the design of the information sources impact network does not allow defining the influence of the information sources on one another accurately and detecting the primary sources of the information…
The Single-Source Shortest Path (SSSP) problem is well-known for the challenges in developing fast, practical, and work-efficient parallel algorithms. This work introduces a novel shortest path search method. It allows paths with different…
Geodesic paths and distances are among the most popular intrinsic properties of 3D surfaces. Traditionally, geodesic paths on discrete polygon surfaces were computed using shortest path algorithms, such as Dijkstra. However, such algorithms…
The problem of finding multiple simple shortest paths in a weighted directed graph $G=(V,E)$ has many applications, and is considerably more difficult than the corresponding problem when cycles are allowed in the paths. Even for a single…
We consider the problem of computing shortest paths in a dense motion-planning roadmap $\mathcal{G}$. We assume that~$n$, the number of vertices of $\mathcal{G}$, is very large. Thus, using any path-planning algorithm that directly searches…
Recent studies show that graph processing systems on a single machine can achieve competitive performance compared with cluster-based graph processing systems. In this paper, we present NXgraph, an efficient graph processing system on a…
Graph neural networks (GNNs) are gaining increasing popularity as a promising approach to machine learning on graphs. Unlike traditional graph workloads where each vertex/edge is associated with a scalar, GNNs attach a feature tensor to…
The notion of vertex sparsification is introduced in \cite{M}, where it was shown that for any graph $G = (V, E)$ and a subset of $k$ terminals $K \subset V$, there is a polynomial time algorithm to construct a graph $H = (K, E_H)$ on just…
The search is based on the preliminary transformation of matrices or adjacency lists traditionally used in the study of graphs into projections cleared of redundant information (refined) followed by the selection of the desired shortest…
A visibility algorithm maps time series into complex networks following a simple criterion. The resulting visibility graph has recently proven to be a powerful tool for time series analysis. However its straightforward computation is…
We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an…
The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of…
We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient…
Vector-based algorithms are novel algorithms in optimal any-angle path planning that are motivated by bug algorithms, bypassing free space by directly conducting line-of-sight checks between two queried points, and searching along obstacle…