Using the Max-Plus Algorithm for Multiagent Decision Making in Coordination Graphs

  • Jelle R. Kok
  • Nikos Vlassis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4020)


Coordination graphs offer a tractable framework for cooperative multiagent decision making by decomposing the global payoff function into a sum of local terms. Each agent can in principle select an optimal individual action based on a variable elimination algorithm performed on this graph. This results in optimal behavior for the group, but its worst-case time complexity is exponential in the number of agents, and it can be slow in densely connected graphs. Moreover, variable elimination is not appropriate for real-time systems as it requires that the complete algorithm terminates before a solution can be reported. In this paper, we investigate the max-plus algorithm, an instance of the belief propagation algorithm in Bayesian networks, as an approximate alternative to variable elimination. In this method the agents exchange appropriate payoff messages over the coordination graph, and based on these messages compute their individual actions. We provide empirical evidence that this method converges to the optimal solution for tree-structured graphs (as shown by theory), and that it finds near optimal solutions in graphs with cycles, while being much faster than variable elimination.


Bayesian Network Joint Action Multiagent System Action Combination Elimination Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jelle R. Kok
    • 1
  • Nikos Vlassis
    • 1
  1. 1.Informatics InstituteUniversity of AmsterdamThe Netherlands

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