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Algorithms and Lower Bounds: A Unified Approach

Objective

One of the fundamental goals of theoretical computer science is to
understand the possibilities and limits of efficient computation. This
quest has two dimensions. The
theory of algorithms focuses on finding efficient solutions to
problems, while computational complexity theory aims to understand when
and why problems are hard to solve. These two areas have different
philosophies and use different sets of techniques. However, in recent
years there have been indications of deep and mysterious connections
between them.

In this project, we propose to explore and develop the connections between
algorithmic analysis and complexity lower bounds in a systematic way.
On the one hand, we plan to use complexity lower bound techniques as inspiration
to design new and improved algorithms for Satisfiability and other
NP-complete problems, as well as to analyze existing algorithms better.
On the other hand, we plan to strengthen implications yielding circuit
lower bounds from non-trivial algorithms for Satisfiability, and to derive
new circuit lower bounds using these stronger implications.

This project has potential for massive impact in both the areas of algorithms
and computational complexity. Improved algorithms for Satisfiability could lead
to improved SAT solvers, and the new analytical tools would lead to a better
understanding of existing heuristics. Complexity lower bound questions are
fundamental
but notoriously difficult, and new lower bounds would open the way to
unconditionally secure cryptographic protocols and derandomization of
probabilistic algorithms. More broadly, this project aims to initiate greater
dialogue between the two areas, with an exchange of ideas and techniques
which leads to accelerated progress in both, as well as a deeper understanding
of the nature of efficient computation.

Field of science

  • /humanities/philosophy, ethics and religion/philosophy
  • /natural sciences/computer and information sciences/artificial intelligence/heuristic programming

Call for proposal

ERC-2013-CoG
See other projects for this call

Funding Scheme

ERC-CG - ERC Consolidator Grants

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
€ 929 824,75
Principal investigator
Rahul Santhanam (Prof.)
Administrative Contact
Gill Wells (Ms.)

Beneficiaries (2)

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
United Kingdom
EU contribution
€ 929 824,75
Address
Wellington Square University Offices
OX1 2JD Oxford
Activity type
Higher or Secondary Education Establishments
Principal investigator
Rahul Santhanam (Prof.)
Administrative Contact
Gill Wells (Ms.)
THE UNIVERSITY OF EDINBURGH

Participation ended

United Kingdom
EU contribution
€ 344 671,25
Address
Old College, South Bridge
EH8 9YL Edinburgh
Activity type
Higher or Secondary Education Establishments
Administrative Contact
Angela Noble (Ms)