Related papers: Distance Preserving Graph Simplification
In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem.…
In the distance query model, we are given access to the vertex set of a $n$-vertex graph $G$, and an oracle that takes as input two vertices and returns the distance between these two vertices in $G$. We study how many queries are needed to…
Persistence diagrams are important tools in the field of topological data analysis that describe the presence and magnitude of features in a filtered topological space. However, current approaches for comparing a persistence diagram to a…
Finding the graphs that are most similar to a query graph in a large database is a common task with various applications. A widely-used similarity measure is the graph edit distance, which provides an intuitive notion of similarity and…
A variety of network modeling problems begin by generating a degree sequence drawn from a given probability distribution. If the randomly generated sequence is not graphic, we give a new approach for generating a graphic approximation of…
In this paper, we study the problem of recovering the latent vertex correspondence between two correlated random graphs with vastly inhomogeneous and unknown edge probabilities between different pairs of vertices. Inspired by and extending…
We investigate the Minimum Eccentricity Shortest Path problem in some structured graph classes. It asks for a given graph to find a shortest path with minimum eccentricity. Although it is NP-hard in general graphs, we demonstrate that a…
Due to their capacity to encode rich structural information, labeled graphs are often used for modeling various kinds of objects such as images, molecules, and chemical compounds. If pattern recognition problems such as clustering and…
A hypergraph is a set V of vertices and a set of non-empty subsets of V, called hyperedges. Unlike graphs, hypergraphs can capture higher-order interactions in social and communication networks that go beyond a simple union of pairwise…
Subgraph matching, which finds subgraphs isomorphic to a query, is the key to information retrieval from data represented as a graph. To avoid redundant exploration in the data, existing methods restrict the search space by extracting…
We develop a framework for algorithms finding the diameter in graphs of bounded distance Vapnik-Chervonenkis dimension, in (parameterized) subquadratic time complexity. The class of bounded distance VC-dimension graphs is wide, including,…
We study two popular ways to sketch the shortest path distances of an input graph. The first is distance preservers, which are sparse subgraphs that agree with the distances of the original graph on a given set of demand pairs. Prior work…
Graph-based data structures have drawn great attention in recent years. The large and rapidly growing trend on developing graph processing systems focuses mostly on improving the performance by preprocessing the input graph and modifying…
Causal discovery aims to recover graphs that represent causal relations among given variables from observations, and new methods are constantly being proposed. Increasingly, the community raises questions about how much progress is made,…
Graph Sparsification aims at compressing large graphs into smaller ones while preserving important characteristics of the input graph. In this work we study Vertex Sparsifiers, i.e., sparsifiers whose goal is to reduce the number of…
This paper deals with the problem of finding a collection of vertex-disjoint paths in a given graph G=(V,E) such that each path has at least four vertices and the total number of vertices in these paths is maximized. The problem is NP-hard…
In this paper, we propose a new data structure for approximate nearest neighbor search. This structure augments the neighborhood graph with a bridge graph. We propose to exploit Cartesian concatenation to produce a large set of vectors,…
Let $P$ be a set of $n \geq 5$ points in convex position in the plane. The path graph $G(P)$ of $P$ is an abstract graph whose vertices are non-crossing spanning paths of $P$, such that two paths are adjacent if one can be obtained from the…
We automatically verify the crucial steps in the original proof of correctness of an algorithm which, given a geometric graph satisfying certain additional properties removes edges in a systematic way for producing a connected graph in…
We consider the problem of finding a Hamiltonian path or cycle with precedence constraints in the form of a partial order on the vertex set. We study the complexity for graph width parameters for which the ordinary problems…