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Strong Convex Relaxations with Optimal Approximation Guarantees

Objective

One of the most exciting areas of theoretical computer science is to understand the approximability of fundamental optimization problems. A prominent example is the traveling salesman problem, for which a long-standing conjecture states that a certain algorithm gives a better guarantee than current methods can prove. The resolution of this conjecture and of many other fundamental problems is intimately related to an increased understanding of strong convex relaxations.

Although these problems have resisted numerous attempts, recent breakthrough results, in which the PI has played a central role, indicate new research directions with the potential to resolve some of our most exciting open questions. We propose three research directions to revolutionize our understanding of these problems and more generally of the use of convex relaxations in approximation algorithms:

(I) develop new approaches to analyze and harness the power of existing convex relaxations;

(II) understand the power of automatically generated relaxations; and

(III) prove the optimality of algorithms based on convex relaxations.

The proposed research lies in the frontier of approximation algorithms and optimization with connections to major problems in complexity theory, such as the unique games conjecture. Any progress will be a significant contribution to theoretical computer science and mathematical optimization.

Call for proposal

ERC-2013-StG
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Address
Batiment Ce 3316 Station 1
1015 Lausanne
Switzerland
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 451 052
Principal investigator
Ola Nils Anders Svensson (Prof.)
Administrative Contact
Caroline Vandevyver (Dr.)

Beneficiaries (1)

ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Switzerland
EU contribution
€ 1 451 052
Address
Batiment Ce 3316 Station 1
1015 Lausanne
Activity type
Higher or Secondary Education Establishments
Principal investigator
Ola Nils Anders Svensson (Prof.)
Administrative Contact
Caroline Vandevyver (Dr.)