A Compact Representation Scheme of Coalitional Games Based on Multi-Terminal Zero-Suppressed Binary Decision Diagrams

  • Yuko Sakurai
  • Suguru Ueda
  • Atsushi Iwasaki
  • Shin-Ichi Minato
  • Makoto Yokoo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7047)

Abstract

Coalitional games, including Coalition Structure Generation (CSG), have been attracting considerable attention from the AI research community. Traditionally, the input of a coalitional game is a black-box function called a characteristic function. Previous studies have found that many problems in coalitional games tend to be computationally intractable in this black-box function representation. Recently, several concise representation schemes for a characteristic function have been proposed. Among them, a synergy coalition group (SCG) has several good characteristics, but its representation size tends to be large compared to other representation schemes.

We propose a new concise representation scheme for a characteristic function based on a Zero-suppressed Binary Decision Diagram (ZDD) and a SCG. We show our scheme (i) is fully expressive, (ii) can be exponentially more concise than the SCG representation, (iii) can solve core-related problems in polynomial time in the number of nodes, and (iv) can solve a CSG problem reasonably well by utilizing a MIP formulation. A Binary Decision Diagram (BDD) has been used as unified infrastructure for representing/manipulating discrete structures in such various domains in AI as data mining and knowledge discovery. Adapting this common infrastructure brings up the opportunity of utilizing abundant BDD resources and cross-fertilization with these fields.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yuko Sakurai
    • 1
  • Suguru Ueda
    • 1
  • Atsushi Iwasaki
    • 1
  • Shin-Ichi Minato
    • 2
  • Makoto Yokoo
    • 1
  1. 1.Kyushu UniversityJapan
  2. 2.Hokkaido UniversityJapan

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