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Let F be a graph. A hypergraph is called Berge-F if it can be obtained by replacing each edge in F by a hyperedge containing it. Let F be a family of graphs. The Turan number of the family Berge-F is the maximum possible number of edges in an r-uniform hyp ...
Given a source of iid samples of edges of an input graph G with n vertices and m edges, how many samples does one need to compute a constant factor approximation to the maximum matching size in G? Moreover, is it possible to obtain such an estimate in a sm ...
Given a graph H and a set of graphs F, let ex(n, H, F) denote the maximum possible number of copies of H in an T-free graph on n vertices. We investigate the function ex(n, H, F), when H and members of F are cycles. Let C-k denote the cycle of length k and ...
Though deep learning (DL) algorithms are very powerful for image processing tasks, they generally require a lot of data to reach their full potential. Furthermore, there is no straightforward way to impose various properties, given by the prior knowledge a ...
Knapsack problems give a simple framework for decision making. A classical example is the min-knapsack problem (MinKnap): choose a subset of items with minimum total cost, whose total profit is above a given threshold. While this model successfully general ...
2-level polytopes naturally appear in several areas of pure and applied mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. In this paper, we present a study of some 2-level polytopes arisi ...
A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, ex ...
A straight-line drawing of a graph G is a mapping which assigns to each vertex a point in the plane and to each edge a straight-line segment connecting the corresponding two points. The rectilinear crossing number of a graph G, (cr) over bar (G), is the mi ...
Suppose that the vertices of a graph G are colored with two colors in an unknown way. The color that occurs on more than half of the vertices is called the majority color (if it exists), and any vertex of this color is called a majority vertex. We study th ...
We present O(log log n)-round algorithms in the Massively Parallel Computation (MPC) model, with a(n) memory per machine, that compute a maximal independent set, a 1 + epsilon approximation of maximum matching, and a 2 + epsilon approximation of minimum ve ...