相关论文: Quilting Stochastic Kronecker Product Graphs to Ge…
There has been a recent explosion in the size of stored data, partially due to advances in storage technology, and partially due to the growing popularity of cloud-computing and the vast quantities of data generated. This motivates the need…
Say that a graph G has property $\mathcal{K}$ if the size of its maximum matching is equal to the order of a minimal vertex cover. We study the following process. Set $N:= \binom{n}{2}$ and let $e_1, e_2, \dots e_{N}$ be a uniformly random…
In this paper, we address the lack of datasets for - and the issue of reproducibility in - collaborative SLAM pose graph optimizers by providing a novel pose graph generator. Our pose graph generator, kollagen, is based on a random walk in…
We present an exact algorithm for computing all common subgraphs with the maximum number of vertices across multiple graphs. Our approach is further extended to handle the connected Maximum Common Subgraph (MCS), identifying the largest…
We study the widely used hierarchical agglomerative clustering (HAC) algorithm on edge-weighted graphs. We define an algorithmic framework for hierarchical agglomerative graph clustering that provides the first efficient $\tilde{O}(m)$ time…
Recent advancements in large language models (LLMs) have shown impressive versatility across various tasks. To eliminate their hallucinations, retrieval-augmented generation (RAG) has emerged as a powerful approach, leveraging external…
We study the computational model where we can access a matrix $\mathbf{A}$ only by computing matrix-vector products $\mathbf{A}\mathrm{x}$ for vectors of the form $\mathrm{x} = \mathrm{x}_1 \otimes \cdots \otimes \mathrm{x}_q$. We prove…
Automatic construction of large knowledge graphs (KG) by mining web-scale text datasets has received considerable attention recently. Estimating accuracy of such automatically constructed KGs is a challenging problem due to their size and…
The graph isomorphism problem asks whether two graphs are identical up to vertex relabeling. While the exact problem admits quasi-polynomial-time classical algorithms, many applications in molecular comparison, noisy network analysis, and…
Quantum annealing (QA) has emerged as a powerful technique to solve optimization problems by taking advantages of quantum physics. In QA process, a bottleneck that may prevent QA to scale up is minor embedding step in which we embed…
In this paper we propose a new approach to detect clusters in undirected graphs with attributed vertices. We incorporate structural and attribute similarities between the vertices in an augmented graph by creating additional vertices and…
We present a $(1+\frac{k}{k+2})$-approximation algorithm for the Maximum $k$-dependent Set problem on bipartite graphs for any $k\ge1$. For a graph with $n$ vertices and $m$ edges, the algorithm runs in $O(k m \sqrt{n})$ time and improves…
This paper introduces MatKG, a novel graph database of key concepts in material science spanning the traditional material-structure-property-processing paradigm. MatKG is autonomously generated through transformer-based, large language…
Given a connected undirected multigraph G (a graph that may contain parallel edges), the algorithm of [19] finds the 3-edge-connected components of $G$ in linear time using an innovative graph contraction technique based on a depth-first…
Finding all maximal $k$-plexes on networks is a fundamental research problem in graph analysis due to many important applications, such as community detection, biological graph analysis, and so on. A $k$-plex is a subgraph in which every…
We introduce a new notion of acyclicity representation in labeled graphs, and present three applications thereof. Our main result is an algorithm that, given a graph $G$ and a $k$-clique expression of $G$, in time $O(6^kn^c)$ counts modulo…
The \emph{$k$-restricted edge-connectivity} of a graph $G$, denoted by $\lambda_k(G)$, is defined as the minimum size of an edge set whose removal leaves exactly two connected components each containing at least $k$ vertices. This graph…
Graph Sampling provides an efficient yet inexpensive solution for analyzing large graphs. While extracting small representative subgraphs from large graphs, the challenge is to capture the properties of the original graph. Several sampling…
Common models for random graphs, such as Erd\H{o}s-R\'{e}nyi and Kronecker graphs, correspond to generating random adjacency matrices where each entry is non-zero based on a large matrix of probabilities. Generating an instance of a random…
Desirable random graph models (RGMs) should (i) reproduce common patterns in real-world graphs (e.g., power-law degrees, small diameters, and high clustering), (ii) generate variable (i.e., not overly similar) graphs, and (iii) remain…