Related papers: Implementing Brouwer's database of strongly regula…
Synthetic data generation has recently gained widespread attention as a more reliable alternative to traditional data anonymization. The involved methods are originally developed for image synthesis. Hence, their application to the…
In this paper, we study a conjecture of Andries E. Brouwer from 1996 regarding the minimum number of vertices of a strongly regular graph whose removal disconnects the graph into non-singleton components. We show that strongly regular…
De Bruijn graphs are essential for sequencing data analysis and must be efficiently constructed and stored for large-scale population studies. They also need to be dynamic to allow updates such as adding or removing edges and nodes.…
Given a complex graph database of node- and edge-attributed multi-graphs as well as associated metadata for each graph, how can we spot the anomalous instances? Many real-world problems can be cast as graph inference tasks where the graph…
For finite abstract simplicial complex $\Sigma$, initial realization $\alpha$ in $\mathbb{E}^d$, and desired edge lengths $L$, we give practical sufficient conditions for the existence of a non-self-intersecting perturbation of $\alpha$…
Generating graphs that are similar to real ones is an open problem, while the similarity notion is quite elusive and hard to formalize. In this paper, we focus on sparse digraphs and propose SDG, an algorithm that aims at generating graphs…
Graph learning algorithms have attained state-of-the-art performance on many graph analysis tasks such as node classification, link prediction, and clustering. It has, however, become hard to track the field's burgeoning progress. One…
We introduce a new concept of a subgraph class called a superbubble for analyzing assembly graphs, and propose an efficient algorithm for detecting it. Most assembly algorithms utilize assembly graphs like the de Bruijn graph or the overlap…
We continue the line of research started in "Broadword Implementation of Rank/Select Queries" proposing broadword (a.k.a. SWAR, "SIMD Within A Register") algorithms for finding matching closed parentheses and the k-th far closed…
Approximate Nearest Neighbor Search (ANNS) in high dimensional space is essential in database and information retrieval. Recently, there has been a surge of interest in exploring efficient graph-based indices for the ANNS problem. Among…
We describe a data structure that maintains the number of triangles in a dynamic undirected graph, subject to insertions and deletions of edges and of degree-zero vertices. More generally it can be used to maintain the number of copies of…
In 2003, van Dam and Haemers posed a fundamental question in spectral graph theory: does there exist a ``sensible'' matrix whose spectrum determines a random graph up to isomorphism? This paper introduces the class of {\em natural graph…
Nowadays, many web databases "hidden" behind their restrictive search interfaces (e.g., Amazon, eBay) contain rich and valuable information that is of significant interests to various third parties. Recent studies have demonstrated the…
Computing the number of realizations of a minimally rigid graph is a notoriously difficult problem. Towards this goal, for graphs that are minimally rigid in the plane, we take advantage of a recently published algorithm, which is the…
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
This thesis focuses on theoretical and algorithmic tools for determining the numbers of induced subgraphs in strongly regular graphs, SRGs, and on further applications of such numbers. We consider in more detail a restricted class of these…
Within a large database G containing graphs with labeled nodes and directed, multi-edges; how can we detect the anomalous graphs? Most existing work are designed for plain (unlabeled) and/or simple (unweighted) graphs. We introduce…
Given a set D of nonnegative integers, we derive the asymptotic number of graphs with a givenvnumber of vertices, edges, and such that the degree of every vertex is in D. This generalizes existing results, such as the enumeration of graphs…
Rigidity theory studies the properties of graphs that can have rigid embeddings in a euclidean space $\mathbb{R}^d$ or on a sphere and which in addition satisfy certain edge length constraints. One of the major open problems in this field…
The rise of powerful generative models has sparked concerns over data authenticity. While detection methods have been extensively developed for images and text, the case of tabular data, despite its ubiquity, has been largely overlooked.…