Related papers: Fast Monotone Summation over Disjoint Sets
In the analysis of large/big data sets, aggregation (replacing values of a variable over a group by a single value) is a standard way of reducing the size (complexity) of the data. Data analysis programs provide different aggregation…
The $k$-SUM problem is given $n$ input real numbers to determine whether any $k$ of them sum to zero. The problem is of tremendous importance in the emerging field of complexity theory within $P$, and it is in particular open whether it…
In bi-criteria optimization problems, the goal is typically to compute the set of Pareto-optimal solutions. Many algorithms for these types of problems rely on efficient merging or combining of partial solutions and filtering of dominated…
This is a discussion of miscellaneous summation, integration and transformation formulas obtained using Fourier analysis. The topics covered are: Series of the form $\sum_{n\in\mathbb{Z}} c_ne^{\pi i \gamma n^2}$; Fusion of integrals, and…
We study summation of sequences and integration in the quantum model of computation. We develop quantum algorithms for computing the mean of sequences which satisfy a p-summability condition and for integration of functions from Lebesgue…
Submodular maximization is a general optimization problem with a wide range of applications in machine learning (e.g., active learning, clustering, and feature selection). In large-scale optimization, the parallel running time of an…
This work proposes an efficient parallel algorithm for non-monotone submodular maximization under a knapsack constraint problem over the ground set of size $n$. Our algorithm improves the best approximation factor of the existing parallel…
We consider the size of large character sums, proving new lower bounds for the quantity $\Delta(N,q) = \sup_{\chi\neq \chi_0 mod q} |\sum_{n < N} \chi(n)|$ for almost all ranges of $N$. The results are proven using the resonance method and…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
Many combinatorial sequences (for example, the Catalan and Motzkin numbers) may be expressed as the constant term of $P(x)^k Q(x)$, for some Laurent polynomials $P(x)$ and $Q(x)$ in the variable $x$ with integer coefficients. Denoting such…
Variational inequalities offer a versatile and straightforward approach to analyzing a broad range of equilibrium problems in both theoretical and practical fields. In this paper, we consider a composite generally non-monotone variational…
Sequence partition problems arise in many fields, such as sequential data analysis, information transmission, and parallel computing. In this paper, we study the following partition problem variant: given a sequence of $n$ items…
We present a polynomial time algorithm, which solves a nonstandard Variation of the well-known PARTITION-problem: Given positive integers $n, k$ and $t$ such that $t \geq n$ and $k \cdot t = {n+1 \choose 2}$, the algorithm partitions the…
Two-level logic minimization is a central problem in logic synthesis, and has applications in reliability analysis and automated reasoning. This paper represents a method of minimizing Boolean sum of products function with binary decision…
We study core-set construction algorithms for the task of Diversity Maximization under fairness/partition constraint. Given a set of points $P$ in a metric space partitioned into $m$ groups, and given $k_1,\ldots,k_m$, the goal of this…
The fast assembling of stiffness and mass matrices is a key issue in isogeometric analysis, particularly if the spline degree is increased. We present two algorithms based on the idea of sum factorization, one for matrix assembling and one…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
This paper presents algorithms for the included-sums and excluded-sums problems used by scientific computing applications such as the fast multipole method. These problems are defined in terms of a $d$-dimensional array of $N$ elements and…
We construct near optimal linear decision trees for a variety of decision problems in combinatorics and discrete geometry. For example, for any constant $k$, we construct linear decision trees that solve the $k$-SUM problem on $n$ elements…
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…