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
- Albert Atserias - Principal Investigator (PI)
- Albert Oliveras - Researcher (Jun 2015 - Sep 2018)
- Szymon Torunczyk - Postdoctoral researcher (Oct 2015 - Apr 2016)
- Joanna Ochremiak - Postdoctoral researcher (Jan 2016 - Dec 2016)
- Massimo Lauria - Postdoctoral researcher (Jan 2016 - Feb 2017)
- Tuomas Hakoniemi - PhD student (Sep 2016 - )
- Michal Garlik - Postdoctoral researcher (Mar 2017 - )
- Ilario Bonacina - Postdoctoral researcher (Sep 2017 - )
- Moritz Müller - Researcher (Jan 2018 - )
- Antoni Lozano - Researcher (Oct 2018 - )
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, France (Jan
29 - Feb 11, 2017)
- Mozhgan Pourmoradnasseri, University of Tartu, Estonia (April 3 - April 4, 2017)
- Joanna Ochremiak, University Paris-Diderot, France (Jun 26 - Jul 7, 2017)
- Stephan Kreutzer, Technische Universität
Berlin (Jul 20 - Jul 31, 2017)
- Phokion Kolaitis, UCSC & IBM Research - Almaden (Nov 12 - Nov 19, 2017)
- Joanna Ochremiak, University Paris-Diderot, France (Jun 26 - Jul
- Joanna Ochremiak, University Paris-Diderot, France (Jan 14 - Jan
- Igor Carboni Oliveira, University of Oxford, UK (May 7 - May
- Massimo Lauria, University of Rome, Italy (May 28 - Jun 8, 2018)
- Joanna Ochremiak, University of Cambridge, UK (Oct 29 - Nov
- Luca Trevisan, University of California, Berkeley, USA (Nov 16 -
Nov 25, 2018)
- Navid Talebanfard, Czech Academy of Sciences, Prague, Czech
Republic (Dec 9 - Dec 16, 2018)
Local Public Activities
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
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.
- Talk at ALBCOM Seminar joint with Barcelona Logic Seminar
by Phokion Kolaitis, Schema Mappings: Structural Propertiers
and Limits, Nov 15, 2017.
- Talk at Workshop JCALM 2018 by Albert Atserias, Two
applications of Ramsey theory to finite model theory, Jan 18,
- Talk at Workshop JCALM 2018 by Moritz Müller, KPT duality
for finite Ramsey degrees, Jan 18,
- Talk at LIMDA Joint Seminar by Igor Carboni Oliveira, Hardness
Magnification for Natural Problems, May 9, 2018.
- Talk at LIMDA Joint Seminar by Luca Trevisan, A Theory of
Spectral Clustering, Nov 21, 2018.
Visitors and members of the team also participate regularly
in the reading group organized
Rué on topics of interest for the project. In the Fall of
2016 the topic was expander
graphs. See here.
In the Fall of 2017 the topics were heterogeneous.
In the Fall of 2018 the topic was non-standard methods for finite
combinatorics. See here.
The contributions by the members of our
- Albert Atserias and Szymon Torunczyk. Non-homogenizable
classes of finite structures. In Proceedings of 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 Proceedings of 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.
- Albert Atserias, Ilario Bonacina, Susanna F. de Rezende,
Massimo Lauria, Jakob Nordström, and Alexander Razborov.
Clique is hard on average for regular resolution,
in Proceedings of 50th Annual ACM Symposium on the
Theory of Computing (STOC), pp. 866-877, Los Angeles, CA, USA, June 2018.
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
and the projects management and contracting office of
- 3 postdoctoral researcher positions, 2 research assistant
positions (with PhD scholarships). May 2015.
- 1 research assistant position (with PhD scholarship). September
- 1 postdoctoral research position. December 2016.
- 2 posdoctoral research positions. March 2017.
- 2 posdoctoral research positions. October 2017.