Related papers: Fast algorithms for differential equations in posi…
In the area of parameterized complexity, to cope with NP-Hard problems, we introduce a parameter k besides the input size n, and we aim to design algorithms (called FPT algorithms) that run in O(f(k)n^d) time for some function f(k) and…
The works presented in this habilitation concern the algorithmics of polynomials. This is a central topic in computer algebra, with numerous applications both within and outside the field - cryptography, error-correcting codes, etc. For…
We establish an improved classical algorithm for solving linear systems in a model analogous to the QRAM that is used by quantum linear solvers. Precisely, for the linear system $A\x = \b$, we show that there is a classical algorithm that…
Packing and covering linear programs belong to the narrow class of linear programs that are efficiently solvable in parallel and distributed models of computation, yet are a powerful modeling tool for a wide range of fundamental problems in…
This paper considers fast algorithms for operations on linearized polynomials. We propose a new multiplication algorithm for skew polynomials (a generalization of linearized polynomials) which has sub-quadratic complexity in the polynomial…
We study algorithms for approximating pairwise similarity matrices that arise in natural language processing. Generally, computing a similarity matrix for $n$ data points requires $\Omega(n^2)$ similarity computations. This quadratic…
We address the question of computing one selected term of an algebraic power series. In characteristic zero, the best algorithm currently known for computing the $N$th coefficient of an algebraic series uses differential equations and has…
We consider the classical problems of interpolating a polynomial given a black box for evaluation, and of multiplying two polynomials, in the setting where the bit-lengths of the coefficients may vary widely, so-called unbalanced…
A fast two-level linearized scheme with unequal time-steps is constructed and analyzed for an initial-boundary-value problem of semilinear subdiffusion equations. The two-level fast L1 formula of the Caputo derivative is derived based on…
Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…
The p-center problem consists in selecting p centers among M to cover N clients, such that the maximal distance between a client and its closest selected center is minimized. For this problem we propose two new and compact integer…
This document contains notes based on lectures given by Hendrik Lenstra at the PCMI summer school 2022. There are many problems in algebraic number theory which one would like to solve algorithmically, for example computation of the maximal…
We initiate the study of sublinear-time algorithms that access their input via an online adversarial erasure oracle. After answering each input query, such an oracle can erase $t$ input values. Our goal is to understand the complexity of…
Recently, several approaches to solving linear systems on a quantum computer have been formulated in terms of the quantum adiabatic theorem for a continuously varying Hamiltonian. Such approaches enabled near-linear scaling in the condition…
For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a…
This papers studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs). It presents a new framework using discrete ODEs as a central tool for computation and provides several implicit characterizations…
The field of computational complexity is concerned both with the intrinsic hardness of computational problems and with the efficiency of algorithms to solve them. Given such a problem, normally one designs an algorithm to solve it and sets…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
Symmetries occur naturally in CSP or SAT problems and are not very difficult to discover, but using them to prune the search space tends to be very challenging. Indeed, this usually requires finding specific elements in a group of…
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…