Related papers: Embedding cover-free families and cryptographical …
We propose a polynomial time construction of an $(n,d)$-universal set over alphabet $\Sigma=\{0,1\}$, of size $d\cdot 2^{d+o(d)}\cdot\log n$. This is an improvement over the size, $d^{5}2^{2.66d}\log n$, of an $(n,d)$-universal set…
A $(v,k,t)$ {\em covering design}, or {\em covering}, is a family of $k$-subsets, called blocks, chosen from a $v$-set, such that each $t$-subset is contained in at least one of the blocks. The number of blocks is the covering's {\em size},…
In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius $\rho$ equal to $3$ or $4$, and are $1/2^i$-th parts, for $i\in\{1,\ldots,u\}$ of binary (respectively, extended…
Most popular word embedding techniques involve implicit or explicit factorization of a word co-occurrence based matrix into low rank factors. In this paper, we aim to generalize this trend by using numerical methods to factor higher-order…
Answering logical queries over incomplete knowledge bases is challenging because: 1) it calls for implicit link prediction, and 2) brute force answering of existential first-order logic queries is exponential in the number of existential…
In this paper, we introduce and develop the circle embedding method. This method hinges essentially on a combinatorial-geometric structure which we choose to call circles of partition. We provide applications in the context of problems that…
External difference families (EDFs) are combinatorial objects which were introduced in the early 2000s, motivated by information security applications such as the construction of AMD codes. Various generalizations have since been defined…
We show algorithms for computing representative families for matroid intersections and use them in fixed-parameter algorithms for set packing, set covering, and facility location problems with multiple matroid constraints. We complement our…
Word embeddings are a powerful approach for capturing semantic similarity among terms in a vocabulary. In this paper, we develop exponential family embeddings, a class of methods that extends the idea of word embeddings to other types of…
We introduce a new method from number fields and codes to construct dense packings in the Euclidean spaces. Via the canonical $\mathbb{Q}$-embedding of arbitrary number field $K$ into $\mathbb{R}^{[K:\mathbb{Q}]}$, both the prime ideal…
First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…
Nested space-filling designs are nested designs with attractive low-dimensional stratification. Such designs are gaining popularity in statistics, applied mathematics and engineering. Their applications include multi-fidelity computer…
At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid,…
Matrix factorization techniques, especially Nonnegative Matrix Factorization (NMF), have been widely used for dimensionality reduction and interpretable data representation. However, existing NMF-based methods are inherently single-scale…
Weak superimposed codes are combinatorial structures related closely to generalized cover-free families, superimposed codes, and disjunct matrices in that they are only required to satisfy similar but less stringent conditions. This class…
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…
The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of…
Finite mixtures of regression models offer a flexible framework for investigating heterogeneity in data with functional dependencies. These models can be conveniently used for unsupervised learning on data with clear regression…
We investigate the problem of safety verification of infinite-state parameterized programs that are formed based on a rich class of topologies. We introduce a new proof system, called parametric proof spaces, which exploits the underlying…
We introduce a definition for \emph{Families of Optimal Binary Non-MDS Erasure Codes} for $[n, k]$ codes over $GF(2)$, and propose an algorithm for finding those families by using hill climbing techniques over Balanced XOR codes. Due to the…