Project description
Research investigates constrained optimisation and satisfaction problems
Constrained optimisation and satisfaction problems (CSPs) are a large family of computational problems that are typically classified as either tractable (solvable in polynomial time) or intractable (NP-hard). However, certain CSPs resist classification, including problems in graph theory, combinatorics and mathematical game theory. The ERC-funded AUTAR project aims to bridge this knowledge gap by analysing candidate algorithms that appear to solve all instances and are not limited to describing hard instances or hardness hypotheses. AUTAR’s innovative approach will build on a recent discovery that two methods from different areas – indistinguishability pebble games from mathematical logic and hierarchies of convex relaxations from mathematical programming – match in strength.
Objective
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.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics discrete mathematics mathematical logic
- natural sciences mathematics applied mathematics game theory
- natural sciences mathematics pure mathematics discrete mathematics graph theory
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
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Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
ERC-COG - Consolidator Grant
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2014-CoG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
08034 BARCELONA
Spain
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