Approximately Dominating Representatives

  • Vladlen Koltun
  • Christos H. Papadimitriou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3363)


We propose and investigate from the algorithmic standpoint a novel form of fuzzy query called approximately dominating representatives or ADRs. The ADRs of a multidimensional point set consist of a few points guaranteed to contain an approximate optimum of any monotone Lipschitz continuous combining function of the dimensions. ADRs can be computed by appropriately post-processing Pareto, or “skyline,” queries [14,1]. We show that the problem of minimizing the number of points returned, for a user-specified desired approximation, can be solved in polynomial time in two dimensions; for three and more it is NP-hard but has a polynomial-time logarithmic approximation. Finally, we present a polynomial-time, constant factor approximation algorithm for three dimensions.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Vladlen Koltun
    • 1
  • Christos H. Papadimitriou
    • 1
  1. 1.Computer Science DivisionUniversity of CaliforniaBerkeleyUSA

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