Related papers: Arithmetic Progression Hypergraphs: Examining the …

We study thresholds for the appearance of a 2-core in random hypergraphs that are a mixture of a constant number of random uniform hypergraphs each with a linear number of edges but with different edge sizes. For the case of two overlapping…

We design improved approximation algorithms for NP-hard graph problems by incorporating predictions (e.g., learned from past data). Our prediction model builds upon and extends the $\varepsilon$-prediction framework by Cohen-Addad, d'Orsi,…

We survey a number of moment hierarchies and test their performances in computing one-dimensional shock structures. It is found that for high Mach numbers, the moment hierarchies are either computationally expensive or hard to converge,…

Subgraph counting is a fundamental primitive in graph processing, with applications in social network analysis (e.g., estimating the clustering coefficient of a graph), database processing and other areas. The space complexity of subgraph…

Despite the recently exhibited importance of higher-order interactions for various processes, few flexible (null) models are available. In particular, most studies on hypergraphs focus on a small set of theoretical models. Here, we…

The theme of this paper is the derivation of analytic formulae for certain large combinatorial structures. The formulae are obtained via fluid limits of pure jump type Markov processes, established under simple conditions on the Laplace…

In many real-world scenarios, an autonomous agent often encounters various tasks within a single complex environment. We propose to build a graph abstraction over the environment structure to accelerate the learning of these tasks. Here,…

Causal and nonparametric estimands in economics and biostatistics can often be viewed as the mean of a linear functional applied to an unknown outcome regression function. Naively learning the regression function and taking a sample mean of…

Data augmentation is practically helpful for visual recognition, especially at the time of data scarcity. However, such success is only limited to quite a few light augmentations (e.g., random crop, flip). Heavy augmentations are either…

We give an analog of the Myhill-Nerode methods from formal language theory for hypergraphs and use it to derive the following results for two NP-hard hypergraph problems: * We provide an algorithm for testing whether a hypergraph has…

Let the random variable $X\, :=\, e(\mathcal{H}[B])$ count the number of edges of a hypergraph $\mathcal{H}$ induced by a random $m$ element subset $B$ of its vertex set. Focussing on the case that $\mathcal{H}$ satisfies some regularity…

Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…

For a directed graph, the Pagerank algorithm emulates a random walker on the graph that occasionally "jumps" to a random vertex based on a jumping parameter $\alpha$. Upon completion, the algorithm generates a stochastic vector whose…

In this paper, we design efficient algorithms to approximately count the number of edges of a given $k$-hypergraph, and to sample an approximately uniform random edge. The hypergraph is not given explicitly, and can be accessed only through…

Quasi-Newton methods refer to a class of algorithms at the interface between first and second order methods. They aim to progress as substantially as second order methods per iteration, while maintaining the computational complexity of…

Counting the number of small patterns is a central task in network analysis. While this problem is well studied for graphs, many real-world datasets are naturally modeled as hypergraphs, motivating the need for efficient hypergraph motif…

Most of the current hypergraph learning methodologies and benchmarking datasets in the hypergraph realm are obtained by lifting procedures from their graph analogs, leading to overshadowing specific characteristics of hypergraphs. This…

The Hough transform (HT) is a fundamental tool across various domains, from classical image analysis to neural networks and tomography. Two key aspects of the algorithms for computing the HT are their computational complexity and accuracy -…

The use of data-random graphs in statistical testing of spatial patterns is introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the points from various classes.…

Counting small patterns in a large dataset is a fundamental algorithmic task. The most common version of this task is subgraph/homomorphism counting, wherein we count the number of occurrences of a small pattern graph $H$ in an input graph…