Bucket and Mini-bucket Schemes for M Best Solutions over Graphical Models

  • Natalia Flerova
  • Emma Rollon
  • Rina Dechter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7205)


The paper focuses on the task of generating the first m best solutions for a combinatorial optimization problem defined over a graphical model (e.g., the m most probable explanations for a Bayesian network). We show that the m-best task can be expressed within the unifying framework of semirings making known inference algorithms defined and their correctness and completeness for the m-best task immediately implied. We subsequently describe elim-m-opt, a new bucket elimination algorithm for solving the m-best task, provide algorithms for its defining combination and marginalization operators and analyze its worst-case performance. An extension of the algorithm to the mini-bucket framework provides bounds for each of the m best solutions. Empirical demonstrations of the algorithms with emphasis on their potential for approximations are provided.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Natalia Flerova
    • 1
  • Emma Rollon
    • 2
  • Rina Dechter
    • 1
  1. 1.University of CaliforniaIrvineUSA
  2. 2.Universitat Politecnica de CatalunyaSpain

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