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Extending Soft Arc Consistency Algorithms to Non-invertible Semirings

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Advances in Artificial Intelligence (MICAI 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6437))

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Abstract

We extend algorithms for arc consistency proposed in the literature in order to deal with (absorptive) semirings that are not 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: among other instances, for those semirings obtained as the cartesian product of any family of semirings. The main application is that the new arc consistency algorithm can be used for multi-criteria soft CSPs. To reach this objective, we first show that any semiring can be transformed into a new 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 (when the × operator of the semiring is not idempotent). We then propose an arc consistency algorithm which takes advantage of this LCD operator.

Supported by the Spanish Ministry of Science and Innovation project TIN 2006-15387-C03-0 and the Italian Ministry of University and Research project PRIN 20089M932N.

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References

  1. Bistarelli, S.: Semirings for Soft Constraint Solving and Programming. LNCS, vol. 2962. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  2. Bistarelli, S., Gadducci, F.: Enhancing constraints manipulation in semiring-based formalisms. In: Brewka, G., Coradeschi, S., Perini, A., Traverso, P. (eds.) ECAI 2006. Frontiers in Artif. Intell. and Applications, vol. 141, pp. 63–67. IOS Press, Amsterdam (2006)

    Google Scholar 

  3. Bistarelli, S., Gadducci, F., Larrosa, J., Rollon, E.: A soft approach to multi-objective optimization. In: de la Banda, M.G., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 764–768. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  4. Bistarelli, S., Montanari, U., Rossi, F.: Semiring-based constraint satisfaction and optimization. Journal of ACM 44(2), 201–236 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bistarelli, S., Pini, M.S., Rossi, F., Venable, K.B.: Bipolar preference problems: Framework, properties and solving techniques. In: Azevedo, F., Barahona, P., Fages, F., Rossi, F. (eds.) CSCLP. LNCS (LNAI), vol. 4651, pp. 78–92. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Cooper, M.: High-order consistency in valued constraint satisfaction. Constraints 10(3), 283–305 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cooper, M., Schiex, T.: Arc consistency for soft constraints. Artificial Intelligence 154(1-2), 199–227 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dechter, R.: Constraint Processing. Morgan Kaufmann, San Francisco (2003)

    MATH  Google Scholar 

  9. Larrosa, J.: Node and arc consistency in weighted CSP. In: AAAI/IAAI 2002, pp. 48–53. AAAI Press, Menlo Park (2002)

    Google Scholar 

  10. Larrosa, J., Meseguer, P.: Exploiting the use of DAC in MAX-CSP. In: Freuder, E.C. (ed.) CP 1996. LNCS, vol. 1118, pp. 308–322. Springer, Heidelberg (1996)

    Google Scholar 

  11. Larrosa, J., Schiex, T.: Solving weighted CSP by maintaining arc consistency. Artificial Intelligence 159(1-2), 1–26 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mackworth, A.K.: Consistency in networks of relations. Artificial Intelligence 8(1), 99–118 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  13. Rossi, F., van Beek, P., Walsh, T.: Handbook of Constraint Programming. Foundations of Artificial Intelligence. Elsevier (2006)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Perugia, Italy

    Stefano Bistarelli & Francesco Santini

  2. Istituto di Informatica e Telematica, CNR Pisa, Italy

    Stefano Bistarelli & Francesco Santini

  3. Dipartimento di Informatica, Università di Pisa, Italy

    Fabio Gadducci

  4. Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Spain

    Javier Larrosa & Emma Rollon

Authors
  1. Stefano Bistarelli
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  2. Fabio Gadducci
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  3. Javier Larrosa
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  4. Emma Rollon
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  5. Francesco Santini
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Editor information

Editors and Affiliations

  1. Instituto Politécnico Nacional, Centro de Investigación en Computación, Av. Juan Dios Batiz, s/n, Zacatenco, 07738, Mexico City, México

    Grigori Sidorov

  2. Area de Computación, Centro de Investigación en Matemáticas (CIMAT), Callejón de Jalisco s/n, Mineral de Valenciana, 36240, Guanajuato, México

    Arturo Hernández Aguirre

  3. Instituto Nacional de Astrofísica, Optica y Electrónica (INAOE), Ciencias Computacionales, Luis Enrique Erro No. 1, 72840, Santa María Tonantzintla, Puebla,, México

    Carlos Alberto Reyes García

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Bistarelli, S., Gadducci, F., Larrosa, J., Rollon, E., Santini, F. (2010). Extending Soft Arc Consistency Algorithms to Non-invertible Semirings. In: Sidorov, G., Hernández Aguirre, A., Reyes García, C.A. (eds) Advances in Artificial Intelligence. MICAI 2010. Lecture Notes in Computer Science(), vol 6437. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16761-4_34

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  • DOI: https://doi.org/10.1007/978-3-642-16761-4_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16760-7

  • Online ISBN: 978-3-642-16761-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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