Funded by

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 ERC2014CoG 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. polynomialtime solvable vs. NPhard. 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 strategydesign 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 hardnesshypotheses that
are stronger but admittedly less robust than NPhardness. 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 hardnesshypotheses. 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.

Team
 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  )
 Alberto Larrauri  PhD student (Sep 2019  )

Visitors (past, current and planned)
 Alexandra Kolla, University of Illinois at UrbanaChampaign, US (Jun 2023, 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 ParisDiderot, France (Jan
29  Feb 11, 2017)
 Mozhgan Pourmoradnasseri, University of Tartu, Estonia (April 3  April 4, 2017)
 Joanna Ochremiak, University ParisDiderot, 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 ParisDiderot, France (Jun 26  Jul
7, 2017)
 Joanna Ochremiak, University ParisDiderot, France (Jan 14  Jan
24, 2018)
 Igor Carboni Oliveira, University of Oxford, UK (May 7  May
18, 2018)
 Massimo Lauria, University of Rome, Italy (May 28  Jun 8, 2018)
 Joanna Ochremiak, University of Cambridge, UK (Oct 29  Nov
9, 2018)
 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)
 Massimo Lauria, University of Rome, Italy (May 9  May 28,
2019)
 Yijia Chen, Fudan University, China (Jul 1  Jul 13,
2019)
 Kousha Etessami, University of Edinburgh, Scotland (Jul 10  Jul
19, 2019)
 Marc Vinyals, Tata Institute for Research, Mumbai, India (Sep 16
 Sep 20, 2019)

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
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 SpaceBounded Setting>, Feb 14, 2017.
 Talk at LIMDA Joint Seminar by Mozhgan Pourmoradnasseri, The (minimum) rank of typical foolingset 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,
2017.
 Talk at Workshop JCALM 2018 by Moritz Müller, KPT duality
for finite Ramsey degrees, Jan 18,
2017.
 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.
 Talk at LIMDA Joint Seminar by Yijia Chen, Shrubdepth, Firstorder
Logic, and Craig's Interpolation Theorem, July 11, 2019.
 Talk at LIMDA Joint Seminar by Marc Vinyals, Equality Alone
Does not Simulate Randomness, Sep 18, 2019.
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.
In the Fall of 2017 the topics were heterogeneous.
See here.
In the Fall of 2018 the topic was nonstandard methods for finite
combinatorics. See here.
The contributions by the members of our
team follow:

Publications
 Albert Atserias and Szymon Torunczyk. Nonhomogenizable
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 firstorder definable
structures. In Proceedings of 36th IARCS Annual Conference on Foundations of Software
Technology and Theoretical Computer Science (FSTTCS 2016), December
1315, 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, 110:1110:14, 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. 866877, Los Angeles, CA, USA, June 2018.

Recruiting
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.
 2 posdoctoral research positions. October 2017.
 2 research assistant positions (with PhD scholarships). June
2019.
