### On the closest string and substring problemsOn the closest string and substring problems

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 Author Li, Ming ♦ Ma, Bin ♦ Wang, Lusheng Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2002 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Closest string and substring ♦ Computer applications ♦ Polynomial-time approximation scheme Abstract The problem of finding a center string that is "close" to everygiven string arises in computational molecular biology and codingtheory. This problem has two versions: the Closest String problemand the Closest Substring problem. Given a set of strings $\textit{S}=$ ${s_{1},$ $s_{2},$ $...,s_{n}},$ each of length $\textit{m},$ the Closest Stringproblem is to find the smallest $\textit{d}$ and a string s of $length\textit{m}$ which is within Hamming distance d to $eachs_{i}$ ε $\textit{S}.$ This problem comes fromcoding theory when we are looking for a code not too far away froma given set of codes. Closest Substring problem, with an additionalinput integer $\textit{L},$ asks for the smallest d and a $string\textit{s},$ of length $\textit{L},$ which is within Hamming distance daway from a substring, of length $\textit{L},$ of each si. This problemis much more elusive than the Closest String problem. The ClosestSubstring problem is formulated from applications in findingconserved regions, identifying genetic drug targets and generatinggenetic probes in molecular biology. Whether there are efficientapproximation algorithms for both problems are major open questionsin this area. We present two polynomial-time approximationalgorithms with approximation ratio 1 + ε for any smallε to settle both questions. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2002-03-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 49 Issue Number 2 Page Count 15 Starting Page 157 Ending Page 171

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Source: ACM Digital Library