lec312 - Suffix Trees checkbld Suffix trees • Linearized...

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Unformatted text preview: Suffix Trees checkbld Suffix trees • Linearized suffix trees • Virtual suffix trees checkbld Suffix arrays • Enhanced suffix arrays • Suffix cactus, suffix vectors, … Suffix Trees • String … any sequence of characters. • Substring of string S … string composed of characters i through j , i <= j of S . square4 S = cater => ate is a substring. square4 car is not a substring. square4 Empty string is a substring of S . Subsequence • Subsequence of string S … string composed of characters i 1 < i 2 < … < i k of S . square4 S = cater => ate is a subsequence. square4 car is a subsequence. square4 The empty string is a subsequence. String/Pattern Matching • You are given a source string S . • Answer queries of the form: is the string p i a substring of S ? • Knuth-Morris-Pratt (KMP) string matching. square4 O(|S| + | p i |) time per query. square4 O(n|S| + Σ i | p i |) time for n queries. • Suffix tree solution. square4 O(|S| + Σ i | p i |) time for n queries. String/Pattern Matching • KMP preprocesses the query string p i , whereas the suffix tree method preprocesses the source string S . • An application of string matching. square4 Genome project. square4 Databank of strings (gene sequences). square4 Character set is ATGF . square4 Determine if a “new” sequence is a substring of a databank sequence....
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lec312 - Suffix Trees checkbld Suffix trees • Linearized...

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