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- W2005964087 abstract "A 1 -median in a finite metric space is a point with the minimum average distance to all other points. Given a positive integer n and oracle access to a distance metric on { 1 , 2 , … , n } , we study the problem of finding a 1 -median. In particular, we show the nonexistence of (1) deterministic O ( 1 ) -approximation o ( n ) -query algorithms, (2) deterministic ( 2 − Ω ( 1 ) ) -approximation o ( n 2 ) -query algorithms for graph metrics, (3) deterministic ( 3 − Ω ( 1 ) ) -approximation o ( n 2 ) -query algorithms and (4) Monte-Carlo ( 2 − Ω ( 1 ) ) -approximation o ( n ) -query algorithms with an Ω ( 1 ) probability of success. We also show a Monte-Carlo ( 2 + ϵ ) -approximation O ( ( log 2 ( 1 / ϵ ) ) / ϵ 3 ) -query algorithm with a 1 − O ( ϵ ) probability of success, where ϵ ∈ ( 0 , 1 ) ." @default.
- W2005964087 created "2016-06-24" @default.
- W2005964087 creator A5043499853 @default.
- W2005964087 date "2012-04-01" @default.
- W2005964087 modified "2023-09-28" @default.
- W2005964087 title "Some results on approximate 1-median selection in metric spaces" @default.
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- W2005964087 doi "https://doi.org/10.1016/j.tcs.2011.12.003" @default.
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