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closest string
In theoretical computer science, closest string is the name of an NP-hard computational problem, which tries to find the geometrical center of a set of input strings.
To understand the word "center" it is necessary to define a distance between two strings. Usually, this problem is studied with the Hamming distance in mind.
==Formal definition==
More formally, given ''n'' length-''m'' strings ''s''1, ''s''2, ..., ''s''''n'', the closest string problem seeks for a new length-''m'' string ''s'' such that ''d''(''s'',''s''''i'') ≤ ''k'' for all ''i'', where ''d'' denotes the Hamming distance, and where ''k'' is as small as possible. A decision problem version of the closest string problem, which is NP-complete, instead takes ''k'' as another input and asks for any string that is within Hamming distance ''k'' of all the input strings.〔
The closest string problem can be seen as an instance of the 1-center problem in which the distances between elements are measured using Hamming distance.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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