Related papers: An in-place, subquadratic algorithm for permutatio…
For most algorithms dealing with sets of points in the plane, the only relevant information carried by the input is the combinatorial configuration of the points: the orientation of each triple of points in the set (clockwise,…
We consider the following problem: given three sets of real numbers, output a word-RAM data structure from which we can efficiently recover the sign of the sum of any triple of numbers, one in each set. This is similar to a previous work by…
The orbit problem is at the heart of symmetry reduction methods for model checking concurrent systems. It asks whether two given configurations in a concurrent system (represented as finite strings over some finite alphabet) are in the same…
In this paper modified variants of the sparse Fourier transform algorithms from [14] are presented which improve on the approximation error bounds of the original algorithms. In addition, simple methods for extending the improved sparse…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
Various decision support systems are available that implement Data Mining and Data Warehousing techniques for diving into the sea of data for getting useful patterns of knowledge (pearls). Classification, regression, clustering, and many…
Computing the convolution $A\star B$ of two length-$n$ vectors $A,B$ is an ubiquitous computational primitive. Applications range from string problems to Knapsack-type problems, and from 3SUM to All-Pairs Shortest Paths. These applications…
Optimal control in general, and flatness-based control in particular, of robotic arms necessitate to compute the first and second time derivatives of the joint torques/forces required to achieve a desired motion. In view of the required…
We have developed an algorithm for transferring radiation in three-dimensional space. The algorithm computes radiation source and sink terms using the Fast Fourier Transform (FFT) method, based on a formulation in which the integral of any…
Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…
This paper studies the \emph{subset sampling} problem. The input is a set $\mathcal{S}$ of $n$ records together with a function $\textbf{p}$ that assigns each record $v\in\mathcal{S}$ a probability $\textbf{p}(v)$. A query returns a random…
In this paper, we introduce a variant of spectral sparsification, called probabilistic $(\varepsilon,\delta)$-spectral sparsification. Roughly speaking, it preserves the cut value of any cut $(S,S^{c})$ with an $1\pm\varepsilon$…
We study the behavior of West's stack-sorting map $s$ on permutations whose last entry is also their least. Let $S_{n}':=\{\pi0\mid \pi\in S_n\}$ where $\pi0$ denotes the concatenation of $\pi$ and $0$. For each permutation $\pi\in S_n'$,…
We give optimal sorting algorithms in the evolving data framework, where an algorithm's input data is changing while the algorithm is executing. In this framework, instead of producing a final output, an algorithm attempts to maintain an…
We revisit the selection problem, namely that of computing the $i$th order statistic of $n$ given elements, in particular the classic deterministic algorithm by grouping and partition due to Blum, Floyd, Pratt, Rivest, and Tarjan (1973).…
A novel integer sorting technique was proposed replacing bucket sort, distribution counting sort and address calculation sort family of algorithms which requires only constant amount of additional memory. The technique was inspired from one…
We study the settings where we are given a function of n variables defined in a given box of integers. We show that in many cases we can replace the given objective function by a new function with a much smaller domain. Our approach allows…
Any permutation-invariant function of data points $\vec{r}_i$ can be written in the form $\rho(\sum_i\phi(\vec{r}_i))$ for suitable functions $\rho$ and $\phi$. This form - known in the machine-learning literature as Deep Sets - also…
Beautiful formulas are known for the expected cost of random two-dimensional assignment problems, but in higher dimensions even the scaling is not known. In three dimensions and above, the problem has natural "Axial" and "Planar" versions,…
Algorithmic efficiency is essential to reducing energy and time usage for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example in stochastic calculations where the size of the random…