Wireless sensor networks (WSNs) and other monitoring systems often use sensors of multiple strengths within the same network. This information is lost when the network is modeled by a typical non-weig...
We study finite and infinite Sidon sets in N^d. The additive energy of two sets is used to obtain new upper bounds for the cardinalities of finite Sidon subsets of some sets as well as to provide shor...
We solve an arithmetic problem due to Erdös and Freud (1986) investigated also by Freiman, Nathanson and Sárközy: How many elements from a given set of integers one must take to represent a power of 2...
We prove that any $r$-coloring of the edges of $K_m$ contains a monochromatic even cycle, where $m = 3r + 1$ if $r$ is odd and $m =3r$ if $r$ is even. We also prove that $K_{m−1}$ has an $r$-coloring ...
We prove several colorful generalizations of classical theorems in discrete geometry. Moreover, the colorful generalization of Kirchberger’s theorem gives a generalization of the theorem of Tverberg o...
We introduce a new concept of dimension for metric spaces, the so-called topological Hausdorff dimension. It is defined by a very natural combination of the definitions of the topological dimension an...
We discuss a structural approach to subset-sum problems in additive combinatorics. The core of this approach are Freiman-type structural theorems, many of which will be presented through the paper. Th...
We consider the problem of generating a connected robust identifying code of a graph, by which we mean a subgraph with two properties: (i) it is connected, (ii) it is robust identifying, in the sense ...
Un code identifiant est un ensemble de sommets d'un graphe tel que, d'une part, chaque sommet hors du code a un voisin dans le code (propriete de domination) et, d'autre part, tous les sommets ont un ...
This paper presents a multi-phase algorithm to solve the global illumination problem. In the first phase dependent tests are applied, i.e. the random walks of different pixels are built from the same ...
The problem of detection of a sparse number of damages in a structure is considered. The idea relies on the newly developed framework for compressed change detection [1], which leverages the unique co...
The paper shows that almost every $n$-vertex graph is, uniquely, determined by its subgraphs with $3 \log_2{n}$ vertices. Therefore, for checking the isomorphism of almost every pair of $n$-vertex gra...
The metric dimension of a graph G is the minimum size of a subset S of vertices of G such that all other vertices are uniquely determined by their distances to the vertices in S . In this paper we inv...
The metric dimension of a graph $G$ is the minimum number of vertices in a subset $S$ of the vertex set of $G$ such that all other vertices are uniquely determined by their distances to the vertices i...
The colourful simplicial depth problem in dimension d is to find a configuration of (d+1) sets of (d+1) points such that the origin is contained in the convex hull of each set, or colour, but containe...
The advent of frequency-agile radios holds the potential for improving the utilization of spectrum by allowing wireless systems to dynamically adapt their spectral footprint based on the local conditi...
Suppose E >O and k > I. We show that if II > n,,(k. a) and .4 L Z,, satisfies IAl > (( l/k) + E)n then there is a subset B L A such that 0 < 1 BI <I, and xhi B h = 0 (in 2,). The case k = 3 solves a p...
Linear rank-width is a linearized variation of rank-width, and it is deeply related to matroid path-width. In this paper, we show that the linear rank-width of every n-vertex distance-hereditary graph...
Let k,m,n⩾2 be integers. Let A be a subset of {0,1,…,n} with 0∈A and the greatest common divisor of all elements of A is 1. Suppose that |A|>1l+12-klmn+2l, where l=⌈k/m⌉. We prove that if m⩾3, or m=...
Let @?, n and r be positive integers. Define F^n={0,1}^n. The Hamming distance between words x and y of F^n is denoted by d(x,y). The ball of radius r is defined as B"r(X)={y@?F^n|@?x@?X:d(x,y)@?r}, w...