Related papers: A Bellman-Ford algorithm for the path-length-weigh…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…
We study a large family of graph covering problems, whose definitions rely on distances, for graphs of bounded cyclomatic number (that is, the minimum number of edges that need to be removed from the graph to destroy all cycles). These…
As the popularity of graph data increases, there is a growing need to count the occurrences of subgraph patterns of interest, for a variety of applications. Many graphs are massive in scale and also fully dynamic (with insertions and…
Evaluating similarity between graphs is of major importance in several computer vision and pattern recognition problems, where graph representations are often used to model objects or interactions between elements. The choice of a distance…
The comparison of graphs is a vitally important, yet difficult task which arises across a number of diverse research areas including biological and social networks. There have been a number of approaches to define graph distance however…
Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R^d. We study the convergence of the shortest path distance in such graphs as the sample size…
We demonstrate that a graph-based search algorithm-relying on the construction of an approximate neighborhood graph-can directly work with challenging non-metric and/or non-symmetric distances without resorting to metric-space mapping…
Given a set $\Omega$ and a proximity function $\phi: \Omega \times \Omega \to \mathbb R^+$, we define a new metric for $\Omega$ by considering a path distance in $\Omega$, that is considered as a complete graph. We analyze the properties of…
A strongly connected digraph is called a cactoid-type if each of its blocks is a digraph consisting of finitely many oriented cycles sharing a common directed path. In this article, we find the formula for the determinant of the distance…
This paper presents the generalization of weighted distances to modules and their computation through the chamfer algorithm on general point lattices. The first part is dedicated to formalization of definitions and properties (distance,…
In this paper we give a single-source shortest-path algorithm that breaks, after over 60 years, the $O(n \cdot m)$ time bound for the Bellman-Ford algorithm, where $n$ is the number of vertices and $m$ is the number of arcs of the graph.…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
In this paper, we present a new metric distance for comparing two large graphs to find similarities and differences between them based on one of the most important graph structural properties, which is Node Adjacency Information, for all…
A {\em parametric weighted graph} is a graph whose edges are labeled with continuous real functions of a single common variable. For any instantiation of the variable, one obtains a standard edge-weighted graph. Parametric weighted graph…
Lifelong SLAM considers long-term operation of a robot where already mapped locations are revisited many times in changing environments. As a result, traditional graph-based SLAM approaches eventually become extremely slow due to the…
The graph edit distance (GED) is a well-established distance measure widely used in many applications. However, existing methods for the GED computation suffer from several drawbacks including oversized search space, huge memory…
In the paper we develop new methods for calculating the two well-known topological indices, the degree-distance and the Gutman index. Firstly, we prove that the Wiener index of a double vertex-weighted graph can be computed from the Wiener…
In weighted graphs the shortest path between two nodes is often reached through an indirect path, out of all possible connections, leading to structural redundancies which play key roles in the dynamics and evolution of complex networks. We…
We study the problem of releasing the weights of all-pair shortest paths in a weighted undirected graph with differential privacy (DP). In this setting, the underlying graph is fixed and two graphs are neighbors if their edge weights differ…
This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a…