Related papers: Distributing hash families with few rows
Covering arrays for words of length $t$ over a $d$ letter alphabet are $k \times n$ arrays with entries from the alphabet so that for each choice of $t$ columns, each of the $d^t$ $t$-letter words appears at least once among the rows of the…
Almost all known secret sharing schemes work on numbers. Such methods will have difficulty in sharing graphs since the number of graphs increases exponentially with the number of nodes. We propose a secret sharing scheme for graphs where we…
Increasingly, biologists are constructing evolutionary trees on large numbers of overlapping sets of taxa, and then combining them into a `supertree' that classifies all the taxa. In this paper, we ask how much coverage of the total set of…
Hashmap is a fundamental data structure in computer science. There has been extensive research on constructing hashmaps that minimize the number of collisions leading to efficient lookup query time. Recently, the data-dependant approaches,…
A hierarchy on a set $S$, also called a total partition of $S$, is a collection $\mathcal{H}$ of subsets of $S$ such that $S \in \mathcal{H}$, each singleton subset of $S$ belongs to $\mathcal{H}$, and if $A, B \in \mathcal{H}$ then $A \cap…
We consider a fashion discounter that supplies any of its many branches with an integral multiple of lots whose size assortment structure stems from a set of many applicable lot-types. We design a column generation algorithm for the optimal…
Perfect codes are arguably the most fascinating structures in combinatorial coding theory, and their classification and weight distribution are of considerable interest. This classification also involves the analysis of some related…
There are several methods for constructing secret sharing schemes, one of which is based on coding theory. Theoretically, every linear code can be used to construct secret sharing schemes. However, in general, determining the access…
It is shown that a normalized complex Hadamard matrix of order $6$ having three distinct columns, each containing at least one $-1$ entry necessarily belongs to the transposed Fourier family, or to the family of $2$-circulant complex…
When solving k-in-a-Row games, the Hales-Jewett pairing strategy [4] is a well-known strategy to prove that specific positions are (at most) a draw. It requires two empty squares per possible winning line (group) to be marked, i.e., with a…
A minimal perfect hash function bijectively maps a key set $S$ out of a universe $U$ into the first $|S|$ natural numbers. Minimal perfect hash functions are used, for example, to map irregularly-shaped keys, such as string, in a compact…
This paper studies distribution-free inference in settings where the data set has a hierarchical structure -- for example, groups of observations, or repeated measurements. In such settings, standard notions of exchangeability may not hold.…
The distributed matrix multiplication problem with an unknown number of stragglers is considered, where the goal is to efficiently and flexibly obtain the product of two massive matrices by distributing the computation across N servers.…
The self-similarity of complex networks is typically investigated through computational algorithms the primary task of which is to cover the structure with a minimal number of boxes. Here we introduce a box-covering algorithm that not only…
We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular…
The $q^k$ (full) factorial design with replication $\lambda$ is the multi-set consisting of $\lambda$ occurrences of each element of each $q$-ary vector of length $k$; we denote this by $\lambda\times [q]^k$. An $m\times n$ row-column…
Consider the following fundamental question of distributed storage networks: Given any arbitrary $(n,k,d)$ values, whether there exists an intelligent helper selection scheme (assuming unlimited memory and computing power) that can strictly…
Consider a large network with unknown number of nodes. Some of these nodes coordinate to perform tasks. The number of such coordination groups is also unknown. The only information about the network available is that any two coordinating…
Secret sharing is an important building block in cryptography. All explicitly defined secret sharing schemes with known exact complexity bounds are multi-linear, thus are closely related to linear codes. The dual of such a linear scheme, in…
In this article, we present a novel box-covering algorithm for analyzing the fractal properties of complex networks. Unlike traditional algorithms that impose a predetermined box size, our approach assigns nodes to boxes identified by their…