Related papers: Compression for trace zero points on twisted Edwar…
We give an optimal-size representation for the elements of the trace zero subgroup of the Picard group of an elliptic or hyperelliptic curve of any genus, with respect to a field extension of any prime degree. The representation is via the…
Using Semaev's summation polynomials, we derive a new equation for the $\mathbb{F}_q$-rational points of the trace zero variety of an elliptic curve defined over $\mathbb{F}_q$. Using this equation, we produce an optimal-size representation…
We consider trace-zero subgroups of elliptic curves over a degree three field extension. The elements of these groups can be represented in compressed coordinates, i.e. via the two coefficients of the line that passes through the point and…
We derive an algorithm for compression of the currents and varifolds representations of shapes, using ridge leverage score (RLS) sampling, and the theory of Nystrom approximation in Reproducing Kernel Hilbert Spaces. Our method is faster…
This paper presents division polynomials for twisted Edwards curves. Their chief property is that they characterise the $n$-torsion points of a given twisted Edwards curve. We also present results concerning the coefficients of these…
We present a novel deep compression algorithm to reduce the memory footprint of LiDAR point clouds. Our method exploits the sparsity and structural redundancy between points to reduce the bitrate. Towards this goal, we first encode the…
We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for…
We study the problem of distance-preserving graph compression for weighted paths and trees. The problem entails a weighted graph $G = (V, E)$ with non-negative weights, and a subset of edges $E^{\prime} \subset E$ which needs to be removed…
This paper presents two kinds of division polynomials for twisted Edwards curves. Their chief property is that they characterise the $n$-torsion points of a given twisted Edwards curve. We also present results concerning the coefficients of…
We propose a framework for discrete scientific data compression based on the tensor-train (TT) decomposition. Our approach is tailored to handle unstructured output data from discrete element method (DEM) simulations, demonstrating its…
Tensor hypercontraction provides an attractive four-center two-electron repulsion integral format that can lower the scaling of many electronic structure methods while only requiring O(N^2) memory. However, in its grid-based least-squares…
This paper describes the adaptation of a well-scaling parallel algorithm for computing Morse-Smale segmentations based on path compression to a distributed computational setting. Additionally, we extend the algorithm to efficiently compute…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
Distributed optimization methods are often applied to solving huge-scale problems like training neural networks with millions and even billions of parameters. In such applications, communicating full vectors, e.g., (stochastic) gradients,…
A novel inline data compression method is presented for single-precision vectors in three dimensions. The primary application of the method is for accelerating computational physics calculations where the throughput is bound by memory…
Efficient point cloud compression is fundamental to enable the deployment of virtual and mixed reality applications, since the number of points to code can range in the order of millions. In this paper, we present a novel data-driven…
Neural-network-based compressors have proven to be remarkably effective at compressing sources, such as images, that are nominally high-dimensional but presumed to be concentrated on a low-dimensional manifold. We consider a continuous-time…
Naturally, with the mounting application of biometric systems, there arises a difficulty in storing and handling those acquired biometric data. Fingerprint recognition has been recognized as one of the most mature and established technique…
This paper presents a novel method to determine rate-distortion optimized transform coefficients for efficient compression of videos generated from point clouds. The method exploits a generalized frequency selective extrapolation approach…
We present two methods to compress the description of a route in a road network, i.e., of a path in a directed graph. The first method represents a path by a sequence of via edges. The subpaths between the via edges have to be unique…