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Mapping the Complexity of Counting

Objective

"Just as advances in engineering rely on a deep foundational knowledge of physics, so too advances in algorithms and programming rely on a deep knowledge of the intrinsic nature of computation. Significant progress has been made, particularly in the field of computational complexity, which aims to discover which computational problems are feasible, which are inherently infeasible, and why. However, huge theoretical challenges remain: many problem classes are poorly understood, including those containing problems arising in practical applications. The MCC project will enable significant computational advances in a host of application areas through the development of a comprehensive theory of counting problems. These problems, which involve the computation of weighted sums, are common and important, arising in practical applications from diverse fields including statistics, statistical physics, information theory, coding, and machine learning. Thus, it is of fundamental importance to understand their complexity. We propose a coherent and systematic study of the complexity of counting problems. A sequence of exciting recent developments, pioneered by the PI and others, makes it plausible that we now have the tools needed to make substantial progress. The overall objectives of MCC are (1) Map out the landscape of computational counting problems (exact and approximate), determining which problems are tractable, and which are intractable (quantifying the extent of tractability), and (2) Develop complexity characterisations elucidating the features that make counting problems tractable or intractable, not only discovering which problems are tractable, but also discovering a characterisation telling us why. The project encompasses a large range of wide-open problems. However, the strength of the PI, the scale of the project, the timeliness of the project (given recent results), and the novel methods proposed make it certain that the research will produce breakthroughs."

Field of science

  • /natural sciences/computer and information sciences/artificial intelligence/machine learning

Call for proposal

ERC-2013-ADG
See other projects for this call

Funding Scheme

ERC-AG - ERC Advanced Grant
Leaflet | Map data © OpenStreetMap contributors, Credit: EC-GISCO, © EuroGeographics for the administrative boundaries

Host institution

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Address
Wellington Square University Offices
OX1 2JD Oxford
United Kingdom
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 2 499 093
Principal investigator
Leslie Ann Goldberg (Prof.)
Administrative Contact
Gill Wells (Ms.)

Beneficiaries (1)

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
United Kingdom
EU contribution
€ 2 499 093
Address
Wellington Square University Offices
OX1 2JD Oxford
Activity type
Higher or Secondary Education Establishments
Principal investigator
Leslie Ann Goldberg (Prof.)
Administrative Contact
Gill Wells (Ms.)