Affiliation:
1. Department of Computer Science and Engineering, Yuan Ze University, Taoyuan, Taiwan
Abstract
Consider the problem of finding a point in a metric space ({ 1,2,…,
n
},
d
) with the minimum average distance to other points. We show that this problem has no deterministic
o
(
n
1+1/(
h
-1)
/
h
)-query 2
h
· (1-ϵ))-approximation algorithms for any constant ϵ >0 and any
h
=
h
(
n
)∈ Z
+
\ {1} satisfying
h
=
o
(
n
1/(
h
-1)
). Combining our result with existing ones, we determine the best approximation ratio achievable by deterministic
O
(
n
1+ϵ
)-query (respectively,
O
(
n
1+ϵ
)-time) algorithms to be 2⌈ 1/ϵ ⌉, for
all
constants ϵ ∈ (0,1).
Funder
Ministry of Science and Technology of Taiwan
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Theory and Mathematics,Theoretical Computer Science
Cited by
4 articles.
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