Skip to main content
Go to the home page of the European Commission (opens in new window)
English English
CORDIS - EU research results
CORDIS

Counting (with) homomorphisms

Objective

This project addresses the computational complexity of counting problems in graphs; such problems ask to compute the number of certain structures rather than merely deciding their existence. Counting problems find applications in diverse areas like network analysis, machine learning, probabilistic databases, and statistical physics. They are linked to fundamental questions in complexity theory and give rise to algorithmic breakthroughs for decision problems.

The proposed project will go beyond the state of the art in computational counting by building bridges between algorithms/complexity and the mathematical theory of graph homomorphisms, which are structure-preserving maps between graphs. Already starting from the 1960s, Lovász and others showed that homomorphism numbers between graphs tie together disparate mathematical areas—similarly, the PI observed in the past 5 years that the computational problem of counting homomorphisms unifies a range of problems in computer science that were previously studied in isolation. This connection allows us to approach fundamental questions in parameterized and fine-grained complexity related to the complexity of counting small patterns in large graphs, which were out of reach for more combinatorial approaches. Secondly, it allows us to revisit problems in classical counting complexity from a new angle, especially for partition functions in discrete physical systems, with the aim of simplifying, unifying and extending known results. Thirdly, homomorphism counts give a surprising novel viewpoint on questions in algebraic complexity surrounding the “permanent versus determinant” problem, an algebraic variant of the “P versus NP” problem.

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.

You need to log in or register to use this function

Keywords

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.

Topic(s)

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.

HORIZON-ERC - HORIZON ERC Grants

See all projects funded under this funding scheme

Call for proposal

Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.

(opens in new window) ERC-2022-STG

See all projects funded under this call

Host institution

UNIVERSITAET REGENSBURG
Net EU contribution

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.

€ 918 676,18
Address
UNIVERSITATSSTRASSE 31
93053 Regensburg
Germany

See on map

Region
Bayern Oberpfalz Regensburg, Kreisfreie Stadt
Activity type
Higher or Secondary Education Establishments
Links
Total cost

The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.

€ 918 676,18

Beneficiaries (2)

My booklet 0 0