hw4 - 4(5 points Microarray oligo design problem Given a...

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BCB 567/CprE 548 Bioinformatics I Fall 2007 Homework 4 Due Tuesday, October 30 1. (5 points) A string S is called semiperiodic with period α if S is a prefix of α k (the substring obtained by concatenating α with itself k times) for some positive integer k . Give an algorithm to find the shortest period of a string S and compute its run time. 2. (5 points) A substring α of a string S is called a minimal unique substring if it satisfies the following properties: α occurs exactly once in S (uniqueness). All proper prefixes of α occur at least twice in S (minimality). The length of α is at least l , for some fixed l . Give an algorithm to enumerate all the minimal unique substrings of a string S . 3. (5 points) Given a string A , a set of strings S , and an integer k , the primer selection problem is the following: For each position i in A , find the shortest substring in A of length at least k that starts in position i and does not occur as a substring of any s ∈ S . Show how to solve this problem in O ( | A | + Σ s ∈S | s | ) time.
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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 k-cover 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 k-cover 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 k-cover, or to determine that no such cover exists....
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