Abstract
Given an n-point metric space (M, d), metric 1-median asks for a point \(p\in M\) minimizing \(\sum _{x\in M}\,d(p,x)\). We show that for each computable function \(f:\mathbb {Z}^+\rightarrow \mathbb {Z}^+\) satisfying \(f(n)=\omega (1)\), metric 1-median has a deterministic, o(n)-query, \(o(f(n)\cdot \log n)\)-approximation and nonadaptive algorithm. Previously, no deterministic o(n)-query o(n)-approximation algorithms are known for metric 1-median.
Supported in part by the Ministry of Science and Technology of Taiwan under grant 109-2221-E-155-031.
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Chang, CL. (2021). Deterministic Metric 1-median Selection with a \(1-o(1)\) Fraction of Points Ignored. In: Chen, CY., Hon, WK., Hung, LJ., Lee, CW. (eds) Computing and Combinatorics. COCOON 2021. Lecture Notes in Computer Science(), vol 13025. Springer, Cham. https://doi.org/10.1007/978-3-030-89543-3_18
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DOI: https://doi.org/10.1007/978-3-030-89543-3_18
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