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Concept

Hardness of approximation

Publications associées (26)

Results on Sparse Integer Programming and Geometric Independent Sets

Jana Tabea Cslovjecsek

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 ...

EPFL2023

Approximate Zero-Crossing: A new interpretable, highly discriminative and low-complexity feature for EEG and iEEG seizure detection

David Atienza Alonso, Tomas Teijeiro Campo, Una Pale, Renato Zanetti

Objective: Long-term monitoring of people with epilepsy based on electroencephalography (EEG) and intracranial EEG (iEEG) has the potential to deliver key clinical information for personalised epilepsy treatment. More specifically, in outpatient settings, ...

2022

Automating cutting planes is NP-hard

Mika Tapani Göös

We show that Cutting Planes (CP) proofs are hard to find: Given an unsatisfiable formula F, It is -hard to find a CP refutation of F in time polynomial in the length of the shortest such refutation; and unless Gap-Hitting-Set admits a nontrivial algorithm, ...

ACM2021

Blind as a bat: spatial perception without sight

Frederike Dümbgen

Among our five senses, we rely mostly on audition and vision to perceive an environment. Our ears are able to detect stimuli from all directions, especially from obstructed and far-away objects. Even in smoke, harsh weather conditions, or at night â situ ...

EPFL2021

Computational Design of Auxetic Shells

Mina Konakovic Lukovic

Recent advances in material science and digital fabrication provide promising opportunities for product design, mechanical and biomedical engineering, robotics, architecture, art, and science. Engineered materials and personalized fabrication are revolutio ...

EPFL2019

Using Structural Properties for Integer Programs

Kim-Manuel Klein

Integer programs (IPs) are one of the fundamental tools used to solve combinatorial problems in theory and practice. Understanding the structure of solutions of IPs is thus helpful to argue about the existence of solutions with a certain simple structure, ...

SPRINGER INTERNATIONAL PUBLISHING AG2018

A Conditional Gradient Framework for Composite Convex Minimization with Applications to Semidefinite Programming

Volkan Cevher, Alp Yurtsever

We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines the notions of smoothing and homotopy under the CGM framework, and provably achieves the optimal O(1/sqrt(k)) convergenc ...

ICML2018

LP-Based Algorithms For Capacitated Facility Location

Ola Nils Anders Svensson

Linear programming (LP) has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of algorithmic me ...

Society for Industrial and Applied Mathematics2017

Constrained bundle methods with inexact minimization applied to the energy regulation provision problem

Colin Neil Jones, Tomasz Tadeusz Gorecki

We consider a class of large scale robust optimization problems. While the robust optimization literature often relies on structural assumptions to reformulate the problem in a tractable form using duality, this method is not always applicable and can resu ...

2017

Near-optimal Deployment of Dataflow Applications on Many-core Platforms with Real-time Guarantees

Alena Simalatsar, Stefanos Skalistis

Safe and optimal deployment of data-streaming applications on many-core platforms requires the realistic estimation of task Worst-Case Execution Time (WCET). On the other hand, task WCET depends on the deployment solution, due to the varying number of inte ...

IEEE2017

A New Framework for Distributed Submodular Maximization

Justin Dean Ward

A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing distributed algo ...

Ieee2016

Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs

Fabio Nobile, Lorenzo Tamellini

In this work we provide a convergence analysis for the quasi-optimal version of the sparse-grids stochastic collocation method we presented in a previous work: “On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods” ...

Springer2016

Strong LP formulations for scheduling splittable jobs on unrelated machines

Ola Nils Anders Svensson

A natural extension of the makespan minimization problem on unrelated machines is to allow jobs to be partially processed by different machines while incurring an arbitrary setup time. In this paper we present increasingly stronger LP-relaxations for this ...

Springer Heidelberg2015

On the configuration LP for maximum budgeted allocation

Ola Nils Anders Svensson, Christos Kalaitzis, Aleksander Madry

We study the maximum budgeted allocation problem, i.e., the problem of selling a set of m indivisible goods to n players, each with a separate budget, such that we maximize the collected revenue. Since the natural assignment LP is known to have an integral ...

Springer Heidelberg2015

An Exact Algorithm to Compute the Double-Cut-and-Join Distance for Genomes with Duplicate Genes

Bernard Moret, Yu Lin, Mingfu Shao

Computing the edit distance between two genomes is a basic problem in the study of genome evolution. The double-cut-and-join (DCJ) model has formed the basis for most algorithmic research on rearrangements over the last few years. The edit distance under t ...

Mary Ann Liebert2015

LP-Based Algorithms for Capacitated Facility Location

Ola Nils Anders Svensson

Linear programming has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of algorithmic methodo ...

IEEE2014

Wireless Network Simplification: The Gaussian N-Relay Diamond Network

Christina Fragouli

We consider the Gaussian N-relay diamond network, where a source wants to communicate to destination node through a layer of N-relay nodes. We investigate the following question: what fraction of the capacity can we maintain using only k out of the N avail ...

Institute of Electrical and Electronics Engineers2014

A quasi-optimal sparse grids procedure for groundwater flows

Fabio Nobile, Lorenzo Tamellini

In this work we explore the extension of the quasi-optimal sparse grids method proposed in our previous work "On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods" to a Darcy problem where the permeability is model ...

Springer2014

Approximation algorithms for regret minimization in vehicle routing problems

Adrian Aloysius Bock

In this thesis, we present new approximation algorithms as well as hardness of approximation results for NP-hard vehicle routing problems related to public transportation. We consider two different problem classes that also occur frequently in areas such a ...

EPFL2014

On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods

Fabio Nobile, Lorenzo Tamellini

In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by mu ...

World Scientific Publ Co Pte Ltd2012