相关论文: A Simple Circle Discretization Algorithm With Appl…
The Cluster Editing problem seeks a transformation of a given undirected graph into a disjoint union of cliques via a minimum number of edge additions or deletions. A multi-parameterized version of the problem is studied, featuring a number…
For general thinning procedures, its inverse operation, the condensing, is studied and a link to integration-by-parts formulas is established. This extends the recent results on that link for independent thinnings of point processes to…
We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…
There are many practical applications that require simplification of polylines. Some of the goals are to reduce the amount of information necessary to store, improve processing time, or simplify editing. The simplification is usually done…
The Chord algorithm is a popular, simple method for the succinct approximation of curves, which is widely used, under different names, in a variety of areas, such as, multiobjective and parametric optimization, computational geometry, and…
In mathematical optimization, we want to find the best possible solution for a decision-making problem. Curiously, these problems are harder to solve if they have discrete decisions. Imagine that you would like to buy chocolate: you can buy…
The discrete cosine transform (DCT) is a relevant tool in signal processing applications, mainly known for its good decorrelation properties. Current image and video coding standards -- such as JPEG and HEVC -- adopt the DCT as a…
We develop a high-order, explicit method for acoustic scattering in three space dimensions based on a combined-field time-domain integral equation. The spatial discretization, of Nystr\"om type, uses Gaussian quadrature on panels combined…
Distance computation is one of the most fundamental primitives used in communication networks. The cost of effectively and accurately computing pairwise network distances can become prohibitive in large-scale networks such as the Internet…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
When applying automatic analysis of fluorescence or histopathological images of cells, it is necessary to partition, or de-clump, partially overlapping cell nuclei. In this work, I describe a method of partitioning partially overlapping…
Symmetries in discrete constraint satisfaction problems have been explored and exploited in the last years, but symmetries in continuous constraint problems have not received the same attention. Here we focus on permutations of the…
Many approaches to 3D image segmentation are based on hierarchical clustering of supervoxels into image regions. Here we describe a distributed algorithm capable of handling a tremendous number of supervoxels. The algorithm works…
Distributions on integers are ubiquitous in probabilistic modeling but remain challenging for many of today's probabilistic programming languages (PPLs). The core challenge comes from discrete structure: many of today's PPL inference…
Normaliz is an open-source software for the computation of lattice points in rational polyhedra, or, in a different language, the solutions of linear diophantine systems. The two main computational goals are (i) finding a system of…
CRCs have desirable properties for effective error detection. But their software implementation, which relies on many steps of the polynomial division, is typically slower than other codes such as weaker checksums. A relevant question is…
Customizing the precision of data can provide attractive trade-offs between accuracy and hardware resources. We propose a novel form of vector computing aimed at arrays of custom-precision floating point data. We represent these vectors in…
Many important applications across science, data analytics, and AI workloads depend on distributed matrix multiplication. Prior work has developed a large array of algorithms suitable for different problem sizes and partitionings including…
We describe a uniformly fast algorithm for generating points \vec{x} uniformly in a hypercube with the restriction that the difference between each pair of coordinates is bounded. We discuss the quality of the algorithm in the sense of its…
G-code (Geometric code) or RS-274 is the most widely used computer numerical control (CNC) and 3D printing programming language. G-code provides machine instructions for the movement of the 3D printer, especially for the nozzle, stage, and…