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Description of the project

AUTAR: A Unified Theory of Algorithmic Relaxations is an ERC CoG (Consolidator Grant) action led by Albert Atserias at Universitat Politècnica de Catalunya. This is a project funded by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement ERC-2014-CoG 648276 AUTAR) for the period June 2015 - May 2020.

Summary: For a large family of computational problems collectively known as constrained optimization and satisfaction problems (CSPs), four decades of research in algorithms and computational complexity have led to a theory that tries to classify them as algorithmically tractable vs. intractable, i.e. polynomial-time solvable vs. NP-hard. However, there remains an important gap in our knowledge in that many CSPs of interest resist classification by this theory. Some such problems of practical relevance include fundamental partition problems in graph theory, isomorphism problems in combinatorics, and strategy-design problems in mathematical game theory. To tackle this gap in our knowledge, the research of the last decade has been driven either by finding hard instances for algorithms that solve tighter and tighter relaxations of the original problem, or by formulating new hardness-hypotheses that are stronger but admittedly less robust than NP-hardness. The ultimate goal of this project is closing the gap between the partial progress that these approaches represent and the original classification project into tractable vs. intractable problems. Our thesis is that the field has reached a point where, in many cases of interest, the analysis of the current candidate algorithms that appear to solve all instances could suffice to classify the problem one way or the other, without the need for alternative hardness-hypotheses. The novelty in our approach is a program to develop our recent discovery that, in some cases of interest, two methods from different areas match in strength: indistinguishability pebble games from mathematical logic, and hierarchies of convex relaxations from mathematical programming. Thus, we aim at making significant advances in the status of important algorithmic problems by looking for a general theory that unifies and goes beyond the current understanding of its components.


  • Albert Atserias - Principal Investigator (PI)
  • Albert Oliveras - Researcher (June 2015 - )
  • Szymon Torunczyk - Postdoctoral researcher (October 2015 - April 2016)
  • Joanna Ochremiak - Postdoctoral researcher (January 2016 - December 2016)
  • Massimo Lauria - Postdoctoral researcher (January 2016 - February 2017)
  • Tuomas Hakoniemi - PhD student (September 2016 - )
  • Michal Garlik - Postdoctoral researcher (March 2017 - )

Visitors (past, current and planned)

  • Alexandra Kolla, University of Illinois at Urbana-Champaign, US (Jun 20-23, 2015)
  • Ilario Bonacina, University of Rome, Italy (Sep 28 - Oct 9, 2015)
  • Michal Garlik, Charles University, Czech Republic (Jun 26 - Jul 3, 2016)
  • Dieter van Melkebeek, University of Wisconsin - Madison, US [on sabbatical leave from UWisc] (Jan 9 - Jun 30, 2017)
  • Ilario Bonacina, KTH Royal Institute of Technology, Sweden (Jan 29 - Feb 18, 2017)
  • Jakob Nordström, KTH Royal Institute of Technology, Sweden (Jan 29 - Feb 4, 2017)
  • Joanna Ochremiak, University Paris Diderot - Paris 7, France (Jan 29 - Feb 11, 2017)
  • Mozhgan Pourmoradnasseri, University of Tartu, Estonia (April 3 - April 4, 2017)
  • Joanna Ochremiak, University Paris Diderot - Paris 7, France (Jun 26 -Jul 7, 2017) 
  • Stephan Kreutzer, Technische Universität Berlin (Jul 20 - Jul 31, 2017)


Visitors funded by the AUTAR project usually contribute a talk on a topic of their expertise and of interest for the project at the ALBCOM Seminar on Algorithms and Theory of Computation of the ALBCOM Research Group. Some of these talks are also announced at the LIMDA Joint Seminar that, besides the ALBCOM Seminar, also includes the COMBGRAPH Seminar on Combinatorics, Graph Theory and Applications, and the DCCG Seminar on Computational Geometry.

  • Talk at ALBCOM Seminar by Alexandra Kolla, Towards Refuting the Unique Games Conjecture, Jun 22, 2015.
  • Talk at LIMDA Joint Seminar by Ilario Bonacina, Strong Size Lower Bounds in Resolution via Games, Oct 1, 2015.
  • Talk at LIMDA Joint Seminar by Szymon Toruczyk, CSPs with infinite instances, Dec 2, 2015.
  • Talk at LIMDA Joint Seminar by Jakob Nordström, How Limited Interaction Hinders Real Communication (and What It Means for Proof and Circuit Complexity, Jan 30, 2017.
  • Talk at LIMDA Joint Seminar by Ilario Bonacina, Total space in Resolution is at least width squared, Feb 6, 2017.
  • Talk at LIMDA Joint Seminar by  Dieter van Melkebeek, Derandomizing Isolation in the Space-Bounded Setting, Feb 14, 2017.
  • Talk at LIMDA Joint Seminar by Mozhgan Pourmoradnasseri, The (minimum) rank of typical fooling-set matrices, April 3, 2017.
  • Talk at LIMDA Joint Seminar by Dieter van Melkebeek, Kernelization lower bounds from AP(3)-free sets, Jun 15, 2017. 
  • Talk at Workshop on Graph Theory and Combinatorics, Foundations of Computational Mathematics 2017 by Albert Atserias, Gaps Between Classical Satisfiability Problem and Their Quantum Relaxations, July 14, 2017.

Both visitors and members of the team also participate regularly in the reading group organized by Juanjo Rué on topics of interest for the project. In the Fall of 2016 the topic was expander graphs. See here for the full list of sessions. The contributions by the members of our team follow:

  • Presentation at reading group by Albert Atserias with title Zig-zag product (I), Dec 1, 2016.
  • Presentation at reading group by Tuomas Hakoniemi with title Zig-zag product (II), Dec 15, 2016.


  • Albert Atserias and Szymon Torunczyk. Non-homogenizable classes of finite structures. In 25th EACSL Annual Conference on Computer Science Logic, CSL 2016, August 29 - September 1, 2016, Marseille, France, pages 16:1–16:16, 2016.
  • Bartek Klin, Slawomir Lasota, Joanna Ochremiak, and Szymon Torunczyk. Homomorphism problems for first-order definable structures. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2016, December 13-15, 2016, Chennai, India, pages 14:1– 14:15, 2016.
  • Albert Atserias and Joanna Ochremiak. Proof Complexity Meets Algebra, in Proceedings of 44th International Colloquium on Automata, Languages, and Programming (ICALP), LIPIcs 80, 110:1--110:14, 2017.


Calls for job applications were announced at the PI's homepage, the Barcelona Graduate School of Mathematics (BGSMath) homepage, the jobs portal of the European Commission EURAXESS, and the projects management and contracting office of UPC CTT.

  • 3 postdoctoral researcher positions, 2 research assistant positions (with PhD scholarships). May 2015.
  • 1 research assistant position (with PhD scholarship). September 2016.
  • 1 postdoctoral research position. December 2016.
  • 2 posdoctoral research positions. March 2017.