The complexity of valued constraints
Lead Research Organisation:
University of Oxford
Department Name: Computer Science
Abstract
This proposal is a collaborative application involving Professor Peter Jeavons at the University of Oxford, Professor David Cohen at Royal Holloway, University of London, and Dr Martin Cooper at the University of Toulouse III, France.We are seeking funding to extend and develop a novel algebraic theory of complexity for valued constraint satisfaction problems.Constraint satisfaction problems arise in many practical problems, such as scheduling and circuit layout, so this family of problems has been widely studied in computer science. All known algorithms for the most general form of the problem require exponential time, and are therefore impractical for large cases. However, several restrictions have been identified which are sufficient to make the restricted form of the problem efficiently solvable. In fact, a careful mathematical analysis of the problem has shown that the computational difficulty of any particular constraint satisfaction problem is closely related to certain algebraic properties of the constraints. In this research project we are seeking to develop a new algebraic approach to an even wider class of problems which involve both constraint satisfaction and optimisation. Such problems are called valued constraint problems. We hope to show that by using general algebraic methods we can identify all types of valued constraints which can be efficiently optimised. We also plan to implement the techniques we develop in new software tools which can be use to analyse any given example of a valued constraint problem, and solve it using special-purpose efficient methods when these are applicable.
Organisations
People |
ORCID iD |
Peter Jeavons (Principal Investigator) |
Publications
Cohen D
(2008)
The expressive power of valued constraints: Hierarchies and collapses
in Theoretical Computer Science
Cohen D
(2011)
Mathematical Foundations of Computer Science 2011
Cohen D
(2013)
An Algebraic Theory of Complexity for Discrete Optimization
in SIAM Journal on Computing
Cooper M
(2010)
Hybrid tractability of soft constraint problems
Cooper M
(2011)
Hybrid tractability of valued constraint problems
in Artificial Intelligence
Cooper M
(2010)
Principles and Practice of Constraint Programming - CP 2010
Cooper M
(2010)
Soft arc consistency revisited
in Artificial Intelligence
Creed P
(2011)
Principles and Practice of Constraint Programming - CP 2011
Creed P
(2010)
The number of Euler tours of a random $d$-in/$d$-out graph
in Discrete Mathematics & Theoretical Computer Science
Zanuttini B
(2009)
A note on some collapse results of valued constraints
in Information Processing Letters