Related papers: Embedding cover-free families and cryptographical …
Roughly speaking, an $(n,(r,s))$-Cover Free Family (CFF) is a small set of $n$-bit strings such that: "in any $d:=r+s$ indices we see all patterns of weight $r$". CFFs have been of interest for a long time both in discrete mathematics as…
Cover-free families were considered from different subjects by numerous researchers. Recently, cover-free families are also found useful in cryptography. In this paper, we use an uniform method to survey known results of cover-free…
Aggregate signatures are used to create one short proof of authenticity and integrity from a set of digital signatures. However, one invalid signature in the set invalidates the entire aggregate, giving no information on which signatures…
An (r;w; d) -cover-free family (CFF) is a family of subsets of a finite set such that the intersection of any r members of the family contains at least d elements that are not in the union of any other w members. The minimum number of…
There is a large literature on cover-free families of finite sets, because of their many applications in combinatorial group testing, cryptographic and communications. This work studies the generalization of cover-free families from sets to…
The paper addresses the problem of defining families of ordered sequences $\{x_i\}_{i\in N}$ of elements of a compact subset $X$ of $R^d$ whose prefixes $X_n=\{x_i\}_{i=1}^{n}$, for all orders $n$, have good space-filling properties as…
A graph is called (generically) rigid in $\mathbb{R}^d$ if, for any choice of sufficiently generic edge lengths, it can be embedded in $\mathbb{R}^d$ in a finite number of distinct ways, modulo rigid transformations. Here we deal with the…
We construct a family of root-finding algorithms which exploit the branched covering structure of a polynomial of degree $d$ with a path-lifting algorithm for finding individual roots. In particular, the family includes an algorithm that…
Maximum distance separable (MDS) codes and near MDS (NMDS) codes are of particular interest in coding theory due to their optimal error-correcting capabilities and wide applications in communication, cryptography, and storage systems. A…
Rough set theory, a mathematical tool to deal with inexact or uncertain knowledge in information systems, has originally described the indiscernibility of elements by equivalence relations. Covering rough sets are a natural extension of…
Theoretical results from discrete geometry suggest that normed spaces can abstractly embed finite metric spaces with surprisingly low theoretical bounds on distortion in low dimensions. In this paper, inspired by this theoretical insight,…
In joint work of the author with Stefan Witzel, a procedure was developed for building new examples of groups in the extended family of R. Thompson's groups, using what we termed \emph{cloning systems}. These new Thompson-like groups can be…
We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…
The study of (minimally) rigid graphs is motivated by numerous applications, mostly in robotics and bioinformatics. A major open problem concerns the number of embeddings of such graphs, up to rigid motions, in Euclidean space. We capture…
In this article, families of non-linear subdivision schemes are presented that are based on univariate polynomials up to degree three. Theses families of schemes are constructed by using dynamic iterative re-weighed least squares method.…
We study the family of intersection graphs of low density objects in low dimensional Euclidean space. This family is quite general, and includes planar graphs. We prove that such graphs have small separators. Next, we present efficient…
Digraph-defined external difference families were recently introduced as a natural generalization of several well-studied combinatorial objects motivated by cryptography (e.g. external difference families (EDFs) and circular external…
The work in this article is concerned with two different types of families of finite sets: separating families and splitting families (they are also called "systems"). These families have applications in combinatorial search, coding theory,…
Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the…
We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…