A Bi-Criteria Approximation Algorithm for k-Means

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

This paper offers a new algorithm to efficiently optimize scheduling decisions for dial-a-ride problems (DARPs), including problem variants considering electric and autonomous vehicles (e-ADARPs). The scheduling heuristic, based on linear programming theor ...

Clustering in education, particularly in large-scale online environments like MOOCs, is essential for understanding and adapting to diverse student needs. However, the effectiveness of clustering depends on its interpretability, which becomes challenging w ...

We introduce an algorithm to reconstruct a mesh from discrete samples of a shape's Signed Distance Function (SDF). A simple geometric reinterpretation of the SDF lets us formulate the problem through a point cloud, from which a surface can be extracted wit ...

Urban proximity planning is foreseen as a solution to foster a “sustainable” city, including economic viability, environmental soundness and social inclusivity. This paper focuses on the inclusivity aspects by questioning the adoption of urban proximities: ...

In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence analysis of collective ...

In light of the challenges posed by climate change and the goals of the Paris Agreement, electricity generation is shifting to a more renewable and decentralized pattern, while the operation of systems like buildings is increasingly electrified. This calls ...

Cutting plane methods are a fundamental approach for solving integer linear programs (ILPs). In each iteration of such methods, additional linear constraints (cuts) are introduced to the constraint set with the aim of excluding the previous fractional opti ...

In this paper, we study sampling from a posterior derived from a neural network. We propose a new probabilistic model consisting of adding noise at every pre- and post-activation in the network, arguing that the resulting posterior can be sampled using an ...

We prove that the Cohn-Elkies linear programming bound for sphere packing is not sharp in dimension 6. The proof uses duality and optimization over a space of modular forms, generalizing a construction of Cohn- Triantafillou [Math. Comp. 91 (2021), pp. 491 ...

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

Graph neural networks (GNNs) have demonstrated promising performance across various chemistry-related tasks. However, conventional graphs only model the pairwise connectivity in molecules, failing to adequately represent higher order connections, such as m ...

We develop a very general version of the hyperbola method which extends the known method by Blomer and Brudern for products of projective spaces to complete smooth split toric varieties. We use it to count Campana points of bounded log-anticanonical height ...

We propose an adaptive quantum algorithm to prepare accurate variational time evolved wave functions. The method is based on the projected variational quantum dynamics (pVQD) algorithm, that performs a global optimization with linear scaling in the number ...

Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...

Distributed learning is the key for enabling training of modern large-scale machine learning models, through parallelising the learning process. Collaborative learning is essential for learning from privacy-sensitive data that is distributed across various ...

For a high-dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in terms of both computational cost and numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g., to the ge ...

The field of biometrics, and especially face recognition, has seen a wide-spread adoption the last few years, from access control on personal devices such as phones and laptops, to automated border controls such as in airports. The stakes are increasingly ...

Robots outside of the fenced factories have to deal with continuously changing environment, this requires fast and flexible modes of control. Planning methods or complex learning models can find optimal paths in complex surroundings, but they are computati ...

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

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 ...

A Bi-Criteria Approximation Algorithm for k-Means

Chat with Graph Search

A ride time-oriented scheduling algorithm for dial-a-ride problems

Interpret3C: Interpretable Student Clustering Through Individualized Feature Selection

Reach For the Arcs: Reconstructing Surfaces from SDFs via Tangent Points

Planning urban proximities: An empirical analysis of how residential preferences conflict with the urban morphologies and residential practices

A multigrid method for PDE-constrained optimization with uncertain inputs

Quantifying the Unknown: Data-Driven Approaches and Applications in Energy Systems

Learning to Remove Cuts in Integer Linear Programming

Gibbs sampling the posterior of neural networks

Six-dimensional sphere packing and linear programming

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Molecular hypergraph neural networks

HYPERBOLA METHOD ON TORIC VARIETIES

Adaptive projected variational quantum dynamics

Scalable constrained optimization

Optimization Algorithms for Decentralized, Distributed and Collaborative Machine Learning

Randomized flexible GMRES with deflated restarting

Performing and Detecting Backdoor Attacks on Face Recognition Algorithms

Exact Obstacle Avoidance for Robots in Complex and Dynamic Environments Using Local Modulation

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Fairness and Explainability in Clustering Problems