Project description
New ground in algorithmic complexity for geometric and algebraic problems
Classic algorithm analysis often struggles to predict performance beyond the worst-case scenario, especially for complex problems involving geometric and algebraic data, including points, vectors, and matrices. While parameterised complexity (PC) has improved understanding in discrete areas such as graphs and Boolean formulas, it has yet to make a big impact on continuous optimisation problems. In this context, the ERC-funded NewPC project will create algorithms that consider multiple key factors influencing their efficiency and accuracy. Specifically, it will rethink tools, including dimension reduction and clustering, through the lens of parameterised complexity. This approach could transform how algorithms are designed in fields ranging from computational geometry and machine learning to optimisation.
Objective
Parameterized Complexity (PC) provides an approach to moving beyond classic worst-case analysis of algorithms by focusing on multivariate algorithms whose performance is influenced by several parameters beyond input size. While it has been successful in various algorithmic domains, particularly those involving discrete objects like graphs, sets, matroids, or Boolean formulas, PC remains underutilized in areas involving geometric and algebraic objects such as points, vectors, linear spaces, or matrices. This project seeks to revolutionize the PC field by developing novel multivariate algorithms for continuous optimization problems involving such objects. The performance of these algorithms—whether measured by approximation ratio, probability error, or running time—is highly sensitive to multiple parameters.
The main challenge in advancing parameterized complexity to these new domains is the need for suitable algorithmic and complexity tools. To address this challenge, the NewPC project proposes to revisit and revise fundamental methods for handling geometric and algebraic objects—such as dimension reduction, sampling, sketching, clustering, and coresets—through the conceptual questions of PC, including determining proper parameterization, quantifying the distance from triviality, and identifying when kernelization is possible.
In short, the proposed Research Program can be summarized as:
Questions of PC + Geometric Methods = New Horizons
The proposed research will open new horizons in parameterized complexity by
- Advancing multivariate approximation and lossy kernelization, both emerging areas within parameterized complexity.
- Establishing multivariate algorithmic analysis as the standard tool for designing provably correct and efficient algorithms in domains such as computational geometry, machine learning, robust statistics, and optimization—areas where the classical worst-case algorithmic analysis often falls short.
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.
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
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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HORIZON.1.1 - European Research Council (ERC)
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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
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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.
HORIZON-ERC - HORIZON ERC Grants
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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-2024-ADG
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5020 Bergen
Norway
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