Related papers: Kinetic $k$-Semi-Yao Graph and its Applications
In this paper we study the computational-statistical gap of the planted clique problem, where a clique of size $k$ is planted in an Erdos Renyi graph $G(n,\frac{1}{2})$ resulting in a graph $G\left(n,\frac{1}{2},k\right)$. The goal is to…
Parametric images provide insight into the spatial distribution of physiological parameters, but they are often extremely noisy, due to low SNR of tomographic data. Direct estimation from projections allows accurate noise modeling,…
The problem of node-similarity in networks has motivated a plethora of such measures between node-pairs, which make use of the underlying graph structure. However, higher-order relations cannot be losslessly captured by mere graphs and…
Finding a list of k teams of experts, referred to as top-k team formation, with the required skills and high collaboration compatibility has been extensively studied. However, existing methods have not considered the specific collaboration…
Let $X$ and $Y$ be any two graphs of order $n$. The friends-and-strangers graph $\mathsf{FS}(X,Y)$ of $X$ and $Y$ is a graph with vertex set consisting of all bijections $\sigma :V(X) \mapsto V(Y)$, in which two bijections $\sigma$,…
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.…
Graph-based approaches are empirically shown to be very successful for the nearest neighbor search (NNS). However, there has been very little research on their theoretical guarantees. We fill this gap and rigorously analyze the performance…
Knowledge Graph Embedding (KGE) aims to represent entities and relations of knowledge graph in a low-dimensional continuous vector space. Recent works focus on incorporating structural knowledge with additional information, such as entity…
A central problem in graph mining is finding dense subgraphs, with several applications in different fields, a notable example being identifying communities. While a lot of effort has been put on the problem of finding a single dense…
Most existing semi-supervised graph-based clustering methods exploit the supervisory information by either refining the affinity matrix or directly constraining the low-dimensional representations of data points. The affinity matrix…
Graphs are fundamental data structures and have been employed for centuries to model real-world systems and phenomena. Random walk with restart (RWR) provides a good proximity score between two nodes in a graph, and it has been successfully…
Approximate K-Nearest Neighbor Search (AKNNS) has now become ubiquitous in modern applications, for example, as a fast search procedure with two tower deep learning models. Graph-based methods for AKNNS in particular have received great…
Sequential dynamical systems (SDS) are used to model a wide range of processes occurring on graphs or networks. The dynamics of such discrete dynamical systems is completely encoded by their phase space, a directed graph whose vertices and…
Vision graph neural networks (ViG) offer a new avenue for exploration in computer vision. A major bottleneck in ViGs is the inefficient k-nearest neighbor (KNN) operation used for graph construction. To solve this issue, we propose a new…
If we pick $n$ random points uniformly in $[0,1]^d$ and connect each point to its $k-$nearest neighbors, then it is well known that there exists a giant connected component with high probability. We prove that in $[0,1]^d$ it suffices to…
Graph Theory and Topological Data Analytics, while powerful, have many drawbacks related to their sensitivity and consistency with TDA & Graph Network Analytics. In this paper, we aim to propose a novel approach for encoding vectorized…
A graph $G$ is said to be $p$-locally dense if every induced subgraph of $G$ with linearly many vertices has edge density at least $p$. A famous conjecture of Kohayakawa, Nagle, R\"odl, and Schacht predicts that locally dense graphs have,…
Two previous papers, arXiv:1803.00284 and arXiv:1803.00281, introduced and studied strong subgraph $k$-connectivity of digraphs obtaining characterizations, lower and upper bounds and computational complexity results for the new digraph…
Approximate nearest neighbor (ANN) search in high-dimensional Euclidean space has a broad range of applications. Among existing ANN algorithms, graph-based methods have shown superior performance in terms of the time-accuracy trade-off.…
Let $D(G)=(d_{ij})_{n\times n}$ denote the distance matrix of a connected graph $G$ with order $n$, where $d_{ij}$ is equal to the distance between vertices $v_{i}$ and $v_{j}$ in $G$. A graph is called distance integral if all eigenvalues…