Local arc consistency for non-invertible semirings, with an application to multi-objective optimization

  • Authors:

  • Stefano Bistarelli;Fabio Gadducci;Javier Larrosa;Emma Rollon;Francesco Santini

  • Affiliations:

  • Dipartimento di Matematica e Informatica, Universití di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy and Istituto di Informatica e Telematica, CNR Pisa, Via Moruzzi 1, 56100 Pisa, Italy;Dipartimento di Informatica, Universití di Pisa, Largo Pontecorvo 3c, 56127 Pisa, Italy;Departament de Llenguatges i Sistemes Informítics, Universitat Politècnica de Catalunya, Campus Diagonal Nord, Edifici (Omega), C. Jordi Girona, 29, 08034 Barcelona, Spain;Departament de Llenguatges i Sistemes Informítics, Universitat Politècnica de Catalunya, Campus Diagonal Nord, Edifici (Omega), C. Jordi Girona, 29, 08034 Barcelona, Spain;Dipartimento di Matematica e Informatica, Universití di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy

  • Venue:
  • Expert Systems with Applications: An International Journal
  • Year:
  • 2012

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Abstract

We extend algorithms for local arc consistency proposed in the literature in order to deal with (absorptive) semirings that may not be invertible. As a consequence, these consistency algorithms can be used as a pre-processing procedure in soft Constraint Satisfaction Problems (CSPs) defined over a larger class of semirings, such as those obtained from the Cartesian product of two (or more) semirings. One important instance of this class of semirings is adopted for multi-objective CSPs. First, we show how a semiring can be transformed into a novel one where the + operator is instantiated with the least common divisor (LCD) between the elements of the original semiring. The LCD value corresponds to the amount we can ''safely move'' from the binary constraint to the unary one in the arc consistency algorithm. We then propose a local arc consistency algorithm which takes advantage of this LCD operator.