Linear-size universal discretization of geometric center-based problems in fixed dimensions
نویسندگان
چکیده
Many geometric optimization problems can be reduced to finding points in space (centers) minimizing an objective function which continuously depends on the distances from centers given input points. Examples are $k$-Means, Geometric $k$-Median/Center, Continuous Facility Location, $m$-Variance, etc. We prove that, for any fixed $\varepsilon>0$, every set of $n$ fixed-dimensional with metric induced by vector norm admits a $O(n)$ candidate computed almost linear time and contains $(1+\varepsilon)$-approximation each point respect all It gives universal approximation-preserving reduction center-based arbitrary continuity-type functions their discrete versions where selected fairly small candidates. The existence such linear-size candidates is also shown doubling dimension.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Optimization
سال: 2021
ISSN: ['1573-2886', '1382-6905']
DOI: https://doi.org/10.1007/s10878-021-00790-6