Related papers: Multidimensional Included and Excluded Sums

Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an…

Biclustering is a powerful data mining technique that allows simultaneously clustering rows (observations) and columns (features) in a matrix-format data set, which can provide results in a checkerboard-like pattern for visualization and…

We present a simple and at the same time fficient algorithm to compute all nondominated extreme points in the outcome set of multi-objective mixed integer linear programmes in any dimension. The method generalizes the well-known dichotomic…

The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…

Impactful applications such as materials discovery, hardware design, neural architecture search, or portfolio optimization require optimizing high-dimensional black-box functions with mixed and combinatorial input spaces. While Bayesian…

In higher-loop calculations, Mellin-Barnes representations are used to simplify the denominators encountered in Feynman parameter integrals. The contour integral of these representations yield sums over residues. We extend the classes of…

The balanced incomplete block design (BIBD) problem is a difficult combinatorial problem with a large number of symmetries, which add complexity to its resolution. In this paper, we propose a dual (integer) problem representation that…

In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…

This paper studies three types of functions arising separately in the analysis of algorithms that we analyze exactly using similar Mellin transform techniques. The first is the solution to a Multidimensional Divide-and-Conquer (MDC)…

In Ultrasound (US) imaging, Delay and Sum (DAS) is the most common beamformer, but it leads to low quality images. Delay Multiply and Sum (DMAS) was introduced to address this problem. However, the reconstructed images using DMAS still…

In recent years, attention has been focused on the relationship between black-box optimiza- tion problem and reinforcement learning problem. In this research, we propose the Mirror Descent Search (MDS) algorithm which is applicable both for…

Consider the classical Min-Sum Set Cover problem: We are given a universe $\mathcal{U}$ of $n$ elements and a collection $\mathcal{S}$ of $k$ subsets of $\mathcal{U}$. Moreover, a cost function is associated with each set. The goal is to…

Recent work by Elmasry et al. (STACS 2015) and Asano et al. (ISAAC 2014), reconsidered classical fundamental graph algorithms focusing on improving the space complexity. We continue this line of work focusing on space. Our first result is a…

Advanced algorithms for large-scale electronic structure calculations are mostly based on processing multi-dimensional sparse data. Examples are sparse matrix-matrix multiplications in linear-scaling Kohn-Sham calculations or the efficient…

The Bin Packing Problem (BPP) has attracted enthusiastic research interest recently, owing to widespread applications in logistics and warehousing environments. It is truly essential to optimize the bin packing to enable more objects to be…

We give efficient algorithms for finding power-sum decomposition of an input polynomial $P(x)= \sum_{i\leq m} p_i(x)^d$ with component $p_i$s. The case of linear $p_i$s is equivalent to the well-studied tensor decomposition problem while…

In many modern data sets, High dimension low sample size (HDLSS) data is prevalent in many fields of studies. There has been an increased focus recently on using machine learning and statistical methods to mine valuable information out of…

Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in…

In the article, within the framework of the Boolean Satisfiability problem (SAT), the problem of estimating the hardness of specific Boolean formulas w.r.t. a specific complete SAT solving algorithm is considered. Based on the well-known…

Combining sum factorization, weighted quadrature, and row-based assembly enables efficient higher-order computations for tensor product splines. We aim to transfer these concepts to immersed boundary methods, which perform simulations on a…