Related papers: Conditional Lower Bounds for Dynamic Geometric Mea…
Many computational problems are subject to a quantum speed-up: one might find that a problem having an O(n^3)-time or O(n^2)-time classic algorithm can be solved by a known O(n^1.5)-time or O(n)-time quantum algorithm. The question…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…
We propose simple polynomial-time algorithms for two linear conic feasibility problems. For a matrix $A\in \mathbb{R}^{m\times n}$, the kernel problem requires a positive vector in the kernel of $A$, and the image problem requires a…
Accurate modeling of boundary conditions is crucial in computational physics. The ever increasing use of neural networks as surrogates for physics-related problems calls for an improved understanding of boundary condition treatment, and its…
We show that a large fraction of the data-structure lower bounds known today in fact follow by reduction from the communication complexity of lopsided (asymmetric) set disjointness. This includes lower bounds for: * high-dimensional…
We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…
We analyse the maximum achievable rate of sustained computation for a given convex region of three dimensional space subject to geometric constraints on power delivery and heat dissipation. We find a universal upper bound across both…
In this paper we present a novel approach for the prescription of high order boundary conditions when approximating the solution of the Euler equations for compressible gas dynamics on curved moving domains. When dealing with curved…
Local Search problem, which finds a local minimum of a black-box function on a given graph, is of both practical and theoretical importance to combinatorial optimization, complexity theory and many other areas in theoretical computer…
This paper presents a new abstract method for proving lower bounds in computational complexity. Based on the notion of topological and measurable entropy for dynamical systems, it is shown to generalise three previous lower bounds results…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems that lead to energy and entropy bounded solutions. A step-by-step procedure for general nonlinear hyperbolic problems on…
In this paper, we study the problem of \textit{constrained} and \textit{stochastic} continuous submodular maximization. Even though the objective function is not concave (nor convex) and is defined in terms of an expectation, we develop a…
In this note, we consider the complexity of maintaining the longest increasing subsequence (LIS) of an array under (i) inserting an element, and (ii) deleting an element of an array. We show that no algorithm can support queries and updates…
Submodular maximization under matroid and cardinality constraints are classical problems with a wide range of applications in machine learning, auction theory, and combinatorial optimization. In this paper, we consider these problems in the…
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…
A model of computation that is widely used in the formal analysis of reactive systems is symbolic algorithms. In this model the access to the input graph is restricted to consist of symbolic operations, which are expensive in comparison to…
We consider several well-studied problems in dynamic algorithms and prove that sufficient progress on any of them would imply a breakthrough on one of five major open problems in the theory of algorithms: 1. Is the 3SUM problem on $n$…
We consider the following problem: given a program, find tight asymptotic bounds on the values of some variables at the end of the computation (or at any given program point) in terms of its input values. We focus on the case of…
Recent methods in ergodic coverage planning have shown promise as tools that can adapt to a wide range of geometric coverage problems with general constraints, but are highly sensitive to the numerical scaling of the problem space. The…