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We propose a Las Vegas probabilistic algorithm to compute the zeta function of a genus-3 hyperelliptic curve defined over a finite field $\mathbb F_q$, with explicit real multiplication by an order $\mathbb Z[\eta]$ in a totally real cubic…
In this article, we design fast algorithms for the computation of approximant bases in shifted Popov normal form. We first recall the algorithm known as PM-Basis, which will be our second fundamental engine after polynomial matrix…
In the literature the empirical characteristic function method is presented as an off-line identification method. While the results of the off-line methods are attractive, the proposed algorithms are ill-conditioned in many cases so that…
We characterize pairs of orthogonal countable ordinals. Two ordinals $\alpha$ and $\beta$ are orthogonal if there are two linear orders $A$ and $B$ on the same set $V$ with order types $\alpha$ and $\beta$ respectively such that the only…
In this paper, we study new batch-dynamic algorithms for the $k$-clique counting problem, which are dynamic algorithms where the updates are batches of edge insertions and deletions. We study this problem in the parallel setting, where the…
Prime-based ordering which is proved to be admissible, is the encoding of indeterminates in power-products with prime numbers and ordering them by using the natural number order. Using Eiffel, four versions of Buchberger's improved…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…
A Las Vegas randomized algorithm is given to compute the Hermite normal form of a nonsingular integer matrix $A$ of dimension $n$. The algorithm uses quadratic integer multiplication and cubic matrix multiplication and has running time…
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…
Prefix aggregation operation (also called scan), and its particular case, prefix summation, is an important parallel primitive and enjoys a lot of attention in the research literature. It is also used in many algorithms as one of the steps.…
We propose a simple O([n^5/\log n]L) algorithm for linear programming feasibility, that can be considered as a polynomial-time implementation of the relaxation method. Our work draws from Chubanov's "Divide-and-Conquer" algorithm [4], where…
Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient…
The paper presents a priori error analysis of the shallow neural network approximation to the solution to the indefinite elliptic equation and and cutting-edge implementation of the Orthogonal Greedy Algorithm (OGA) tailored to overcome the…
Algorithmic pricing is the computational problem that sellers (e.g., in supermarkets) face when trying to set prices for their items to maximize their profit in the presence of a known demand. Guruswami et al. (2005) propose this problem…
In this paper we consider a logical treatment for the ordered disjunction operator 'x' introduced by Brewka, Niemel\"a and Syrj\"anen in their Logic Programs with Ordered Disjunctions (LPOD). LPODs are used to represent preferences in logic…
While theoretical computer science primarily works with discrete models of computation, like the Turing machine and the wordRAM, there are many scenarios in which introducing real computation models is more adequate. We want to compare real…
In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…
We present and mathematically analyze an online adjoint algorithm for the optimization of partial differential equations (PDEs). Traditional adjoint algorithms would typically solve a new adjoint PDE at each optimization iteration, which…
Hierarchical clustering is a widely used approach for clustering datasets at multiple levels of granularity. Despite its popularity, existing algorithms such as hierarchical agglomerative clustering (HAC) are limited to the offline setting,…