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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…
Let V denote a set of N vertices. To construct a "hypergraph process", create a new hyperedge at each event time of a Poisson process; the cardinality K of this hyperedge is random, with arbitrary probability generating function r(x),…
A regular partition $\mathcal{P}$ for a $3$-uniform hypergraph $H=(V,E)$ consists of a partition $V=V_1\cup \ldots \cup V_t$ and for each $ij\in {[t]\choose 2}$, a partition $K_2[V_i,V_j]=P_{ij}^1\cup \ldots \cup P_{ij}^{\ell}$, such that…
Given a set $S$ of $n$ keys, a perfect hash function for $S$ maps the keys in $S$ to the first $m \geq n$ integers without collisions. It may return an arbitrary result for any key not in $S$ and is called minimal if $m = n$. The most…
Learning a hidden hypergraph is a natural generalization of the classical group testing problem that consists in detecting unknown hypergraph $H_{un}=H(V,E)$ by carrying out edge-detecting tests. In the given paper we focus our attention…
Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…
An uncertain graph $\mathcal{G} = (V, E, p : E \rightarrow (0,1])$ can be viewed as a probability space whose outcomes (referred to as \emph{possible worlds}) are subgraphs of $\mathcal{G}$ where any edge $e\in E$ occurs with probability…
The Harary-Hill conjecture states that for every $n>0$ the complete graph on $n$ vertices $K_n$, the minimum number of crossings over all its possible drawings equals \begin{align*} H(n) :=…
Entity linking (EL) is the task of linking a textual mention to its corresponding entry in a knowledge base, and is critical for many knowledge-intensive NLP applications. When applied to tables in scientific papers, EL is a step toward…
Hash coding has been widely used in the approximate nearest neighbor search for large-scale image retrieval. Recently, many deep hashing methods have been proposed and shown largely improved performance over traditional…
Locality-sensitive hashing converts high-dimensional feature vectors, such as image and speech, into bit arrays and allows high-speed similarity calculation with the Hamming distance. There is a hashing scheme that maps feature vectors to…
Numerical homogenization aims to efficiently and accurately approximate the solution space of an elliptic partial differential operator with arbitrarily rough coefficients in a $d$-dimensional domain. The application of the inverse operator…
In the Hedge Cut problem, the edges of a graph are partitioned into groups called hedges, and the question is what is the minimum number of hedges to delete to disconnect the graph. Ghaffari, Karger, and Panigrahi [SODA 2017] showed that…
We show that a randomly chosen linear map over a finite field gives a good hash function in the $\ell_\infty$ sense. More concretely, consider a set $S \subset \mathbb{F}_q^n$ and a randomly chosen linear map $L : \mathbb{F}_q^n \to…
Finding inherent or processed links within a dataset allows to discover potential knowledge. The main contribution of this article is to define a global framework that enables optimal knowledge discovery by visually rendering co-occurences…
Recent advances in random linear systems on finite fields have paved the way for the construction of constant-time data structures representing static functions and minimal perfect hash functions using less space with respect to existing…
In modern datasets, where single records can have multiple owners, enforcing user-level differential privacy requires capping each user's total contribution. This "contribution bounding" becomes a significant combinatorial challenge.…
Discovering dense subgraphs and understanding the relations among them is a fundamental problem in graph mining. We want to not only identify dense subgraphs, but also build a hierarchy among them (e.g., larger but sparser subgraphs formed…
Hash-based sampling and estimation are common themes in computing. Using hashing for sampling gives us the coordination needed to compare samples from different sets. Hashing is also used when we want to count distinct elements. The quality…
We give exact relations for certain types of the hierarchic fractal structures. In the blatant distinction from regular networks of the "small world" (SW) topology [1], regular fractal networks manifests the logarithmic dependence of the…