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In this paper we provide faster algorithms for solving the geometric median problem: given $n$ points in $\mathbb{R}^{d}$ compute a point that minimizes the sum of Euclidean distances to the points.
The Theory of the Location of Industries
Alfred Weber · 1909
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Sur le point pour lequel la somme des distances de n points donnes est minimum
E. Weiszfeld · 1937
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A note on fermat’s problem
HaroldW. Kuhn · 1973
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On the convergence of a class of iterative methods for solving the weber location problem
Lawrence M. Ostresh · 1978
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The alias and alias-rejection-mixture methods for generating random variables from probability distributions
Richard A. Kronmal and Arthur V. Peterson · 1979
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The weber problem revisited
Leon Cooper and I.Norman Katz · 1981
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A note on the weiszfeld-kuhn algorithm for the general fermat problem
Egon Balas and Chang-Sung Yu · 1982
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The algebraic degree of geometric optimization problems
Chanderjit Bajaj · 1988
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A polynomial-time algorithm, based on newton’s method, for linear programming
James Renegar · 1988
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Open questions concerning weiszfeld’s algorithm for the fermat-weber location problem
R. Chandrasekaran and A. Tamir · 1989
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Breakdown points of affine equivariant estimators of multivariate location and covariance matrices
Hendrik P. Lopuhaa and Peter J. Rousseeuw · 1991
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Breakdown points of affine equivariant estimators of multivariate location and covariance matrices
Hendrik P Lopuhaa and Peter J Rousseeuw · 1991
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Path-following methods for linear programming
Clovis C Gonzaga · 1992
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Interior-point polynomial algorithms in convex programming
Yurii Nesterov and Arkadii Semenovich Nemirovskii · 1994
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On torricelli’s geometrical solution to a problem of fermat
Jakob Krarup and Steven Vajda · 1997
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An efficient algorithm for minimizing a sum of euclidean norms with applications
Guoliang Xue and Yinyu Ye · 1997
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High-dimensional computational geometry
P. Indyk and Stanford University. Computer Science Dept · 2000
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Fast approximations for sums of distances, clustering and the Fermat-Weber problem
Prosenjit Bose, Anil Maheshwari, and Pat Morin · 2003
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Introductory Lectures on Convex Optimization: A Basic Course
Yu Nesterov · 2003
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Smaller coresets for k-median and k-means clustering
Sariel Har-Peled and Akash Kushal · 2005
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On the convergence of the weiszfeld algorithm for continuous single facility location allocation problems
Frank Plastria and Mohamed Elosmani · 2008
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A unified framework for approximating and clustering data
Dan Feldman and Michael Langberg · 2011
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Zvi Drezner, Kathrin Klamroth, Anita Schöbel, and George Wesolowsky · 2002
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De maximis et minimis geometrica divinatio liber 2
Vincenzo Viviani
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Runtime guarantees for regression problems
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