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. Fields of science natural sciencescomputer and information sciencescomputational science Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-SG-PE6 - ERC Starting Grant - Computer science and informatics 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 EU contribution € 1 451 052,00 Address BATIMENT CE 3316 STATION 1 1015 Lausanne Switzerland See on map Region Schweiz/Suisse/Svizzera Région lémanique Vaud Activity type Higher or Secondary Education Establishments Administrative Contact Caroline Vandevyver (Dr.) Principal investigator Ola Nils Anders Svensson (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE Switzerland EU contribution € 1 451 052,00 Address BATIMENT CE 3316 STATION 1 1015 Lausanne See on map Region Schweiz/Suisse/Svizzera Région lémanique Vaud Activity type Higher or Secondary Education Establishments Administrative Contact Caroline Vandevyver (Dr.) Principal investigator Ola Nils Anders Svensson (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data