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The Exact Approximation Ratio of Uniformly Rotated Coordinate-wise Median in the Euclidean Plane

Zichen, Song
arXiv (All) · Papers
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and-sciencecomputational-engineeringcomputer-science-and-game-theoryfinance
Uniformly rotated coordinate-wise median chooses a random orthonormal coordinate system, takes a median in each coordinate, and maps the resulting point back to the Euclidean plane. We determine its exact worst-case expected approximation ratio when social cost is the $L_p$ norm of the agents' Eucli
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