This project ended on Sep 30, 2020
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Funded by
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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 (extended until
September 2020 due to COVID-19 outbreak).
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.
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Team
- Albert Atserias - Principal Investigator (PI)
- Moritz Müller - Researcher (Jan 2018 - Sep 2020)
- Szymon Toruńczyk - Researcher (Oct 2015 - Apr 2016)
- Albert Oliveras - Researcher (Jun 2015 - Sep 2018)
- Antoni Lozano - Researcher (Oct 2018 - May 2020)
- Joanna Ochremiak - Postdoctoral researcher (Jan 2016 - Dec 2016)
- Massimo Lauria - Postdoctoral researcher (Jan 2016 - Feb 2017)
- Michal Garlik - Postdoctoral researcher (Mar 2017 - Sep 2020)
- Ilario Bonacina - Postdoctoral researcher (Sep 2017 - Sep 2020)
- Tuomas Hakoniemi - Research assistant, PhD student (Sep 2016 -
Dec 2019)
- Alberto Larrauri - Research assistant, PhD student (Sep 2019 -
Sep 2020)
- Ely Piceno - Research assistant, PhD student (Oct 2019 - Sep 2020)
- Gabriel Verdejo - IT staff (Jun 2015 - Sep 2020)
- Ivan Couto - IT staff (Jun 2015 - Sep 2020)
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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
7, 2017)
- Joanna Ochremiak, University Paris-Diderot, 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)
- Joanna Ochremiak, Univesity of Bordeaux and CNRS, France (Jan 25
- Apr 30, 2020)
- Nathanaël Fijalkow, Univesity of Bordeaux and CNRS, France (Jan 25
- Apr 30, 2020)
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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 Toruńczyk, 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,
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, Shrub-depth, First-order
Logic, and Craig's Interpolation Theorem, Jul 11, 2019.
- Talk at LIMDA Joint Seminar by Marc Vinyals, Equality Alone
Does not Simulate Randomness, Sep 18, 2019.
- Talk at LIMDA Joint Seminar by Or Zamir, Faster k-SAT
algorithms using biased-PPSZ, Jun 25, 2020.
Visitors and members of the team also participate regularly
in the reading group organized
by Juanjo
Rué no topics of interest for the project. In the Fall of
2016 the topic was expander
graphs. See here.
In the Spring of 2017 the topic was graph limits. See
here.
In the Fall of 2017 the topics were heterogeneous.
See here.
In the Fall of 2018 the topic was non-standard methods for finite
combinatorics. See here.
In the Fall of 2019 the topic was random walks over groups.
See here.
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.
- Presentation at reading group by Ilario Bonacina with title
Deterministic search for CNF satisfying assignments in almost
polynomial time, by Servedio and Tan, Feb 28, 2018.
- Presentation at reading group by Moritz Müller of Appendix
and Chapters 1 and 2 of Nonstandard Methods in Ramsey
Theory and Combinatorial Number Theory (1/3), Sep 12, 2018.
- Presentation at reading group by Moritz Müller of Appendix
and Chapters 1 and 2 of Nonstandard Methods in Ramsey
Theory and Combinatorial Number Theory (2/3), Sep 19, 2018.
- Presentation at reading group by Moritz Müller of Appendix
and Chapters 1 and 2 of Nonstandard Methods in Ramsey
Theory and Combinatorial Number Theory (3/3), Oct 3, 2018.
- Presentation at reading group by Alberto Larrauri of
the Carne-Varopoulos Inequality from Random
walks on Infinite Discrete Groups, Oct 29, 2019.
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Organization of events
The PI has been involved into
the organization of several scientific events of relevance to the
topics of the AUTAR project. We list them here:
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The Oberwolfach Workshop on Proof Complexity and Beyond
was held in Oberwolfach Research Institute for Mathematics,
Oberwolfach-Walke, Germany, on August 13-19, 2017. The PI was part of the
Organizing and Scientific Committee. The members of the group
Atserias, Lauria, and Ochremiak contributed talks to the workshop.
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The Dagstuhl
Seminar on Proof Complexity was held in Schloss Dagstuhl,
Leibniz-Zentrum für Informatik, on January 28 - February 2,
2018. The PI was part of the Organizing and Scientific Committee. The
members of the group Atserias, Bonacina, and Müller (as well as
past members Lauria and Ochremiak) contributed talks at the
workshop.
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The Banff
Workshop on Proof Complexity was held in Banff International
Research Center (BIRS), Banff, Alberta, Canada, on January 19--24,
2020. The PI was part of the Organizing and Scientific Committee. The
members of the group Atserias, Bonacina, Garlík and Hakoniemi
attended and contributed talks to the workshop.
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Publications
- Bartek Klin, Slawomir Lasota, Joanna Ochremiak, and Szymon
Toruńczyk. 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), Chennai,
India, LIPIcs 65, pages 14:1– 14:15, Dec 2016. Repository version.
- Albert Atserias and Joanna Ochremiak. Proof Complexity Meets Algebra,
ACM Transactions on Computational Logic, 20(1), pages 1:1--1:46,
2019. A preliminary version appeared in
Proceedings of 44th International Colloquium on Automata, Languages,
and Programming (ICALP), LIPIcs 80, 110:1--110:14, 2017. Repository version.
- Albert Atserias, Phokion G. Kolaitis, and Simone Severini. Generalized
Satisfiability Problems via Operator Assignments.
Journal of Computer and System Sciences, 105, pages 171--198, 2019. A
preliminary version appeared in proceedings of 21st International
Symposium on Fundamentals of Computation Theory (FCT
2017), Lecture
Notes in Computer Science, 10472, pages 56-68, 2017. Best
Paper Award. Repository version.
- 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. Repository version.
- Albert Atserias, Stephan Kreutzer, and Marc Noy. On Zero-One and Convergence Laws for Graphs Embeddable on a Fixed
Surface, in Proceedings of 45th
International Colloquium on Automata, Languages, and Programming
(ICALP), Leibniz International Proceedings in Informatics (LIPIcs),
116:1--116:14, Prague, Czech, July 2018. Repository version.
- Albert Atserias and Moritz Müller.
Automating Resolution is NP-Hard. Journal of the ACM, Vol. 67,
No. 5, Article No. 31, September 2020. Preliminary version in
Proceedings of
60th Annual IEEE Symposium on Foundations of Computer Science (FOCS
2019), pages 498-509, 2019. Co-winner of Best paper award. Repository version.
- Albert Atserias, Anuj Dawar, and Joanna Ochremiak.
On the Power of Symmetric Linear Programs. In
Proceedings of 34th Annual ACM/IEEE Symposium on Logic in Computer
Science (LICS 2019), Vancouver, BC, Canada, pages 1-13, Jun 2019.
Repository version.
- Albert Atserias and Massimo Lauria.
Circular (Yet Sound) Proofs.
In Proceedings of 22nd International Conference on Theory and Applications
of Satisfiability Testing (SAT 2019), Lisbon, Portugal, pages 1-18,
Jul 2019. Repository version.
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Recruiting
Calls for
job applications were announced at
the PI's institutional
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 postdoctoral research positions. March 2017.
- 2 postdoctoral research positions. October 2017.
- 2 research assistant positions (with PhD scholarships). June
2019.
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