English

Metric $1$-median selection: Query complexity vs. approximation ratio

Computational Complexity 2015-09-21 v1

Abstract

Consider the problem of finding a point in a metric space ({1,2,,n},d)(\{1,2,\ldots,n\},d) with the minimum average distance to other points. We show that this problem has no deterministic o(n1+1/(h1))o(n^{1+1/(h-1)})-query (2hΩ(1))(2h-\Omega(1))-approximation algorithms for any constant hZ+{1}h\in\mathbb{Z}^+\setminus\{1\}.

Keywords

Cite

@article{arxiv.1509.05662,
  title  = {Metric $1$-median selection: Query complexity vs. approximation ratio},
  author = {Ching-Lueh Chang},
  journal= {arXiv preprint arXiv:1509.05662},
  year   = {2015}
}
R2 v1 2026-06-22T10:59:54.930Z