Database Theory - ICDT 2005

Volume 3363 of the series Lecture Notes in Computer Science pp 204-214

Approximately Dominating Representatives

  • Vladlen KoltunAffiliated withComputer Science Division, University of California
  • , Christos H. PapadimitriouAffiliated withComputer Science Division, University of California

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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.