Applied Databases. Sebastian Maneth. Lecture 13 Online Pattern Matching on Strings. University of Edinburgh - February 29th, 2016
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1 Applied Dtses Lecture 13 Online Pttern Mtching on Strings Sestin Mneth University of Edinurgh - Ferury 29th, 2016
2 2 Outline 1. Nive Method 2. Automton Method 3. Knuth-Morris-Prtt Algorithm 4. Boyer-Moore Algorithm
3 3 Full-Text Serch tokenize nturl lnguge documents uild inverted files execute keyword-queries over inverted files rnk results ccording to TFIDF-sed scoring
4 4 Full-Text Serch tokenize nturl lnguge documents uild inverted files execute keyword-queries over inverted files rnk results ccording to TFIDF-sed scoring Limits of this pproch: serch over DNA sequences huge sequence over C, T, G A (c. 3.2 illion) no spces, no tokens...
5 5 Pttern Mtching on Strings serch over DNA sequences huge sequence over C, T, G A (c. 3.2 illion) no spces, no tokens... Given long string T (text) short string P (pttern) Prolem 1: Prolem 2: [ often: over fixed lphet ] find ll occurrences of P in T count #occurrence of P in T
6 6 Pttern Mtching on Strings serch over DNA sequences huge sequence over C, T, G A (c. 3.2 illion) no spces, no tokens... Given long string T (text) short string P (pttern) Prolem 1: Prolem 2: [ often: over fixed lphet ] find ll occurrences of P in T count #occurrence of P in T Two versions: offline = we my index T, efore running the serch online = directly run serch (e.g., T not stored, comes in strem) [ we my index P, this is clled preprocessing ]
7 7 Pttern Mtching on Strings Highlights Online Serch: O( T ) time with O( P ) preprocessing Offline Serch: O( P + #occ) time with O( T ) preprocessing Given long string T (text) short string P (pttern) Prolem 1: Prolem 2: find ll occurrences of P in T count #occurrence of P in T Two versions: offline = we my index T, efore running the serch online = directly run serch (e.g., T not stored, comes in strem) [ we my index P, this is clled preprocessing ]
8 8 Online Pttern Mtching on Strings Given short string P (pttern) long string T (text) Prolem 1: Prolem 2: my preprocess P! find ll occurrences of P in T count #occurrence of P in T 1) Automton Method uild mtch utomton A for P nd run A over T 2) Knuth-Morris-Prtt Algorithm uild jump-tle for P nd use it when trversing T 3) Boyer-Moore Algorithm similr to KMP, ut mtch ckwrds in P
9 9 1. Nive Method Given Pttern P, Text T, find ll occurrences of P in T.
10 10 1. Nive Method Given Pttern P, Text T, find ll occurrences of P in T.
11 11 1. Nive Method Given Pttern P, Text T, find ll occurrences of P in T.
12 12 1. Nive Method Given Pttern P, Text T, find ll occurrences of P in T.
13 13 1. Nive Method Given Pttern P, Text T, find ll occurrences of P in T.
14 14 1. Nive Method Given Pttern P, Text T, find ll occurrences of P in T.
15 15 1. Nive Method Given Pttern P, Text T, find ll occurrences of P in T.
16 16 1. Nive Method Given Pttern P, Text T, find ll occurrences of P in T.
17 17 Some Definitions Word v is suffix of word w, if w = uv for some u. ( proper suffix, if u is non-empty) Word u is prefix of w, if w = uv for some v. ( proper prefix, if v is non-empty) Word u is fctor of w, if there re v nd v such tht w = vuv
18 18 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch c 5 mismtch mens not if chrcter set C is known, then for every c in C {}, we hve one trnsition d(0, c) = 0
19 19 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch mismtch mens not nd not 3 4 c 5
20 20 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch 0 1 mismtch c 5
21 21 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch 0 1 mismtch c 5
22 22 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch c 5 mismtch -trnsition where should it go???
23 23 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch mismtch why? ecuse is the longest suffix of, tht is prefix of c 5
24 24 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch 0 1 mismtch c 5
25 25 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch mismtch Deterministic Finite Automton O( P S ) size, where S = lphet 3 4 c 5
26 26 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch c 5 mismtch Deterministic Finite Automton O( P S ) size, where S = lphet simply run it in O( T ) time to determine ll occurrences of P in T
27 27 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch 0 1 mismtch c 5
28 28 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch 0 1 mismtch c 5
29 29 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch 0 1 mismtch c 5
30 30 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch 0 1 mismtch c 5
31 31 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch 0 1 mismtch c 5
32 32 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch 0 1 mismtch c 5
33 33 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch 0 1 mismtch c 5
34 34 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch 0 1 mismtch c 5
35 35 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch 0 1 mismtch c 5
36 36 2. Automton Method Given Pttern P, Text T, find ll occurrences of P in T. mismtch 0 1 mismtch c 5 Mtch!
37 37 2. Automton Method Given Pttern P, how to uild the utomton? for stte k nd symol x, how to uild trnsition d(k,x)? length of the longest proper suffix of P[1] P[x]x tht is prefix of P E.g. d(4, ) =?
38 38 2. Automton Method Given Pttern P, how to uild the utomton? for stte k nd symol x, how to uild trnsition d(k,x)? length of the longest proper suffix of P[1] P[x]x tht is prefix of P E.g. d(4, ) =? P[1]...P[4] = proper suffix
39 39 2. Automton Method Given Pttern P, how to uild the utomton? for stte k nd symol x, how to uild trnsition d(k,x)? length of the longest proper suffix of P[1] P[x]x tht is prefix of P E.g. d(4, ) =? P[1]...P[4] = is lso prefix! proper suffix
40 40 2. Automton Method Given Pttern P, how to uild the utomton? for stte k nd symol x, how to uild trnsition d(k,x)? length of the longest proper suffix of P[1] P[x]x tht is prefix of P E.g. d(4, ) = 3 = length( ) P[1]...P[4] = is lso prefix! proper suffix Lopopre(u, v) = longest proper suffix of u tht is prefix of v
41 41 Drwck of Automton Method mtching time: O(n) nice! n = T m = P preprocessing time: O(m * S ) cn e O(m * m) not so nice... (for lrge ptterns) Idelly would like to hve O(n) mtching time or O(n + m) O(m) preprocessing time
42 42 3. Knuth-Morris-Prtt Algorithm Brief History: 1970: Jmes H. Morris uilt text editor for the CDC 6400 computer with Vughn Prtt, developed A liner pttern mtching lgorithm [Report 40, University of Cliforni, Berkely, 1970] Mtching time: O(n + m)
43 43 3. Knuth-Morris-Prtt Algorithm Brief History: 1970: Jmes H. Morris uilt text editor for the CDC 6400 computer with Vughn Prtt, developed A liner pttern mtching lgorithm [Report 40, University of Cliforni, Berkely, 1970] Mtching time: O(n + m) rigorous nlysis (Knuth) reveled: dely t chrcter cn e O(m) Knuth dded one check to Morris&Prtt s conditions, ws then le to prove logrithmic dely (tight ound) #chrcter comprisons is <= 2n-1
44 44 3. Knuth-Morris-Prtt Algorithm Jmes H. Morris uilt text editor for the CDC 6400 computer with Vughn Prtt, developed A liner pttern mtching lgorithm [Report 40, University of Cliforni, Berkely, 1970] 1977
45 45 3. Morris-Prtt (1970) Given Pttern P, Text T, find ll occurrences of P in T.
46 46 3. Morris-Prtt (1970) Given Pttern P, Text T, find ll occurrences of P in T.
47 47 3. Morris-Prtt (1970) Given Pttern P, Text T, find ll occurrences of P in T.
48 48 3. Morris-Prtt (1970) Given Pttern P, Text T, find ll occurrences of P in T.
49 49 3. Morris-Prtt (1970) Given Pttern P, Text T, find ll occurrences of P in T.
50 50 3. Morris-Prtt (1970) Given Pttern P, Text T, find ll occurrences of P in T. Lopopre(P[1..j], P)
51 51 3. Morris-Prtt (1970) Given Pttern P, Text T, find ll occurrences of P in T. Lopopre(P[1..j], P)
52 52 3. Morris-Prtt (1970) Given Pttern P, Text T, find ll occurrences of P in T. Lopopre(P[1..j], P)
53 53 3. Morris-Prtt (1970) Given Pttern P, Text T, find ll occurrences of P in T. Lopopre(P[1..j], P)
54 54 3. Morris-Prtt (1970) Given Pttern P, Text T, find ll occurrences of P in T. Lopopre(P[1..j], P)
55 55 3. Morris-Prtt (1970) Given Pttern P, Text T, find ll occurrences of P in T. Lopopre(P[1..j], P)
56 56 3. Morris-Prtt (1970) Given Pttern P, Text T, find ll occurrences of P in T.
57 57 3. Morris-Prtt (1970) Given Pttern P, Text T, find ll occurrences of P in T. dely = 3
58 58 3. Knuth-Morris-Prtt lrgest
59 59 3. Knuth-Morris-Prtt lrgest
60 60 3. Knuth-Morris-Prtt lrgest
61 61 3. Knuth-Morris-Prtt lrgest
62 62 3. Knuth-Morris-Prtt Mtching complexity of KMP: O(m+n) [sme s for KP] wht is the mximum dely for KMP?
63 63 3. Knuth-Morris-Prtt Mtching complexity of KMP: O(m+n) [sme s for KP] wht is the mximum dely for KMP?
64 64 3. Knuth-Morris-Prtt
65 65 4. Boyer-Moore Roert S. Boyer nd J. Strother Moore in 1977
66 66 4. Boyer-Moore
67 67 4. Boyer-Moore Wht hppens if T[5]= z?
68 68 4. Boyer-Moore Wht hppens if T[5]= z? cn shift ll the wy to T[6]!
69 69 4. Boyer-Moore Wht hppens if T[5]= z? cn shift ll the wy to T[6]! never ever consider letters T[1], T[2], T[3], T[4]!!!
70 70 4. Boyer-Moore Wht hppens if T[5]= z? cn shift ll the wy to T[6]! never ever consider letters T[1], T[2], T[3], T[4]!!! cn chieve su-liner mtching time!
71 71
72 72 END Lecture 13
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