Related papers: The Shortest-Path distance on graphons
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
Given an undirected graph $G=(V,E)$ with positive edge lengths and two vertices $s$ and $t$, the next-to-shortest path problem is to find an $st$-path which length is minimum amongst all $st$-paths strictly longer than the shortest path…
The Wiener index of a graph is the sum of all pairwise shortest-path distances between its vertices. In this paper we study the novel problem of finding a minimum Wiener connector: given a connected graph $G=(V,E)$ and a set $Q\subseteq V$…
In this work, we explore the interplay between graph limit theory, the geometry of underlying probability spaces, spectral theory, and network dynamical systems. We investigate two primary questions concerning forward and inverse…
Graphene was recently proposed as a material for heat removal owing to its extremely high thermal conductivity. We simulated heat propagation in silicon-on-insulator circuits with and without graphene lateral heat spreaders. Numerical…
We study the concept of the continuous mean distance of a weighted graph. For connected unweighted graphs, the mean distance can be defined as the arithmetic mean of the distances between all pairs of vertices. This parameter provides a…
Riemannian optimization uses local methods to solve optimization problems whose constraint set is a smooth manifold. A linear step along some descent direction usually leaves the constraints, and hence retraction maps are used to…
This paper discusses the shortest path problem in a general directed graph with $n$ nodes and $K$ cost scenarios (objectives). In order to choose a solution, the min-max criterion is applied. The min-max version of the problem is hard to…
For a connected graph $G$ and $\alpha\in [0,1)$, the distance $\alpha$-spectral radius of $G$ is the spectral radius of the matrix $D_{\alpha}(G)$ defined as $D_{\alpha}(G)=\alpha T(G)+(1-\alpha)D(G)$, where $T(G)$ is a diagonal matrix of…
In this paper, we leverage the properties of non-Euclidean Geometry to define the Geodesic distance (GD) on the space of statistical manifolds. The Geodesic distance is a real and intuitive similarity measure that is a good alternative to…
Shortest-path roadmaps, also known as reduced visibility graphs, provides a highly efficient multi-query method for computing optimal paths in two-dimensional environments. Combined with Minkowski sum computations, shortest-path roadmaps…
The Fr\'echet distance is a distance measure between trajectories in $\Bbb{R}^d$ or walks in a graph $G$. Given constant-time shortest path queries, the Discrete Fr\'echet distance $D_G(P, Q)$ between two walks $P$ and $Q$ can be computed…
In this paper we determine the unique graph with minimum distance spectral radius among all connected graphs of fixed order and given edge connectivity.
Mapping the thermal transport properties of materials at the nanoscale is of critical importance for optimizing heat conduction in nanoscale devices. Several methods to determine the thermal conductivity of materials have been developed,…
Let $P$ be a simple polygon with $n$ vertices. For any two points in $P$, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in $P$. Given a set $S$ of $m$ sites being a subset…
With the aid of the relaxed polygonal inequality (introduced by Fagin et al.) we strive to extend the applicability of Christofides approximation technique to the scope of all complete finite weighted graphs with positive weights. First…
The {\em metric dimension} of a graph $\Gamma$ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. We consider the Grassmann graph…
In data analysis, there is a strong demand for graph metrics that differ from the classical shortest path and resistance distances. Recently, several new classes of graph metrics have been proposed. This paper presents some of them…
A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph. A plethora of shortest-path algorithms is studied in the literature that span across multiple disciplines. This paper presents a survey of…
Let $G=(V,E)$ be a connected graph. The distance between two vertices $u,v\in V$, denoted by $d(u, v)$, is the length of a shortest $u-v$ path in $G$. The distance between a vertex $v\in V$ and a subset $P\subset V$ is defined as $min\{d(v,…