Abstract
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.
Work on this paper was supported by an NSF ITR grant and a France-Berkeley Foundation grant.
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Koltun, V., Papadimitriou, C.H. (2004). Approximately Dominating Representatives. In: Eiter, T., Libkin, L. (eds) Database Theory - ICDT 2005. ICDT 2005. Lecture Notes in Computer Science, vol 3363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30570-5_14
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DOI: https://doi.org/10.1007/978-3-540-30570-5_14
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