Unifying Arc Consistency for Semiring-Based Constraint Satisfaction and Optimization


Tomáš Werner
22nd Conf. on Operational Research, Prague
July, 2007

Abstract

(Soft) constraint satisfaction problems are general problems of combinatorial optimization. They can be uni ed by algebraic formulation, e.g., by using two abstract operations forming a commutative semiring. A fundamental concept to tackle the crisp CSP is arc consistency. We generalize arc consistency to some soft CSPs and formulate it the semiring framework. We newly introduce sum-product arc consistency and give its relation to max-sum arc consistency and optimal max-sum arc consistency. We give a criterion that decreases after every arc consistency iteration.


Bibtex entry

@Proceedings{Werner-EURO07,
  author =       {Tom{\'a}{\vs} Werner},
  title =     {Unifying Arc Consistency for Semiring-Based Constraint Satisfaction and Optimization},
  month =     {July},
  year =      {2007},
  booktitle = {22nd Conf. on Operational Research, Prague},
  note =      {Invited talk.},
  annote = {(Soft) constraint satisfaction problems are general
  problems of combinatorial optimization. They can be uni ed by
  algebraic formulation, e.g., by using two abstract operations
  forming a commutative semiring. A fundamental concept to tackle the
  crisp CSP is arc consistency. We generalize arc consistency to some
  soft CSPs and formulate it the semiring framework. We newly
  introduce sum-product arc consistency and give its relation to
  max-sum arc consistency and optimal max-sum arc consistency. We give
  a criterion that decreases after every arc consistency
  iteration.},
}