Approximately Dominating Representatives

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.

• Type: Conference
• Year: 2005
• Where: ICDT
• Authors: Vladlen Koltun, Christos H. Papadimitriou
• Keywords: Constant Factor Approximation Algorithm, Database, ICDT 2005, Polynomial-time Logarithmic Approximation, User-specified Desired Approximation