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This paper addresses the complexity reduction of stochastic homogenization of a class of random materials for a stationary diffusion equation. A cost-efficient approximation of the correctors is obtained using a method designed to exploit quasi-periodicity ...
In this thesis, we give new approximation algorithms for some NP-hard problems arising in resource allocation and network design. As a resource allocation problem, we study the Santa Claus problem (also known as the MaxMin Fair Allocation problem) in which ...
An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n.Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed p ...
Background: Although digital mobility outcomes (DMOs) can be readily calculated from real-world data collected with wearable devices and ad-hoc algorithms, technical validation is still required. The aim of this paper is to comparatively assess and validat ...
Control systems operating in real-world environments often face disturbances arising from measurement noise and model mismatch. These factors can significantly impact the perfor- mance and safety of the system. In this thesis, we aim to leverage data to de ...
Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...
In this thesis we present and analyze approximation algorithms for three different clustering problems. The formulations of these problems are motivated by fairness and explainability considerations, two issues that have recently received attention in the ...
Submodular functions are a widely studied topic in theoretical computer science. They have found several applications both theoretical and practical in the fields of economics, combinatorial optimization and machine learning. More recently, there have also ...
We study the basic problem of assigning memoryless workers to tasks with dynamically changing demands. Given a set of w workers and a multiset T ⊆ [t] of |T| = w tasks, a memoryless worker-task assignment function is any function ϕ that assigns the workers ...
Schloss Dagstuhl -- Leibniz-Zentrum fur Informatik2022
We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...