Unformatted text preview: 4. (5 points) Microarray oligo design problem: Given a set S = { s 1 ,s 2 ,...,s m } of m strings of total length n , identify m substrings α 1 ,α 2 ,...,α m , such that each substring α i satisﬁes the following: (a) Uniqueness: α i is a substring of s i , and is not a substring of any other string in S . (b) Size: α i is the shortest substring of s i that satisﬁes (a). 5. (10 points) You are given two strings S 1 and S 2 and a parameter k . A kcover of S 2 is a sequence of substrings of S 1 , each of length ≥ k , which when concatenated together give S 2 ; i.e., T 1 ,T 2 ,T 3 ,...,T l is a kcover iﬀ  T i  ≥ k , T i is a substring of S 1 (1 ≤ i ≤ l ), and S 2 = T 1 k T 2 k T 3 k ... k T l , where  denotes the concatenation operation. The substrings may overlap in S 1 . Give a linear time algorithm to ﬁnd kcover, or to determine that no such cover exists....
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 Fall '06
 OLIVEREULENSTEIN
 Natural number, Quantification, TI, Substring

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