Fast String Searching. J Strother Moore Department of Computer Sciences University of Texas at Austin
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1 Fast String Searching J Strother Moore Department of Computer Sciences University of Texas at Austin 1
2 The Problem One of the classic problems in computing is string searching: find the first occurrence of one character string ( the pattern ) in another ( the text ). Generally, the text is very large (e.g., gigabytes) but the patterns are relatively small. 2
3 Examples Find the word comedy in this NY Times article: Fred Armisen s office at Saturday Night Live is deceptively small, barely big enough to fit a desk, a couch, and an ipod. The glorified closet, the subject of a running joke on the comedy show, now in its 31st season, can simultaneously house a wisecracking... 3
4 AAAAAAAAAAAAACAAAGACAGGGGCAACAAAGTGAGACCCTAAAAAAAAAAAAACCCCA AAACGGAGAACTTGGAATCCTGTGTCCAAAAAAAAAAGCAGGAAGAGAGCGTGTAGAAAC TGAAGCTGAAGTGGAAAAAAAAAAGTCGCCAGCACCTACTGTGGAGACCAGAAAGGAAAA AAAAAATTGGCAGTCTCGTAGCATACCAAAACTAGGCTTGAAAAAAAAAACACACAAAAA AACACAGGCTACCCAGTATTTTATCGTCCAAAAAAAAAGAGGGAAGAAGGACATTTATAT TTGCCTTCTGCCAAAAAAAAAAGTACCTCCCGCCTAGAAGAGAGTTTAGAAATCACCAAA AAAAAATAGAGAGTCCCAAAATGTTCGGAATACTCAGAAAAAAAAATCTTAGTCAGTGCT CACTCAGAGGGACCGGGTATTTAAAAAAAACCTAGACCAGATGCAGCAGGTACAAATTAA TCAATCCCAAAAAAAAGACCTTCTACCCTTCCAAAAAATGATAGTTGTCTGCAATCCAAA AAAAAGACTCTCCGGAAGGTGGACATGCAGAACCTACCAAAAAAAAAGAGAAGAAAGAAT TGCCGGGCAAAAAGTTCCACGTAAAAAAAAAAGGAAATGGGAATGGAGTGTTGTTCTCCT TCCTACCTAGTTTTGAAAAAAAAGGATGGATGTGGGTCACCTGCTCACGTTCTCCAAAAA AAAGTGGGTGCTCTCTCACAATATTCTTAGAGGTGGCAAAAAAAATAAAGTTGATGGAAA CAGTACTGTGTGGGCCAAACAAAAAAAAAATGGCACCACCTTTTCATTGGCTGAAAAAAA AATTCAACTGAAAAACACAAGTCATACCTTCCTGTTTTATTTGCAAAAAAAATTTTTCAA ACCCCACGGCAACAAACGACAGTATCAAAAAAACAACTTCATTTGACATTCTGCTATATT AATGCTCTATGTGGAAAAAAAAACCATCAAGTTGTGCCTTTTTTCAAAGAAATCCATGCA AAAAAAAGACCCATGAAATAATTTTCTGGATCATCCATACAGAACCAAAAAAAAGAGGTG 4
5 5
6 Variants of the problem allow wildcards in the pattern and/or the text. Exact matching is when no wildcards are allowed. We describe the fastest sequential algorithm for solving the exact string searching problem. The algorithm is called the Boyer-Moore fast string searching algorithm. 6
7 Example Find the word comedy in this NY Times article: Fred Armisen s office at Saturday Night Live is deceptively small, barely big enough to fit a desk, a couch, and an ipod. The glorified closet, the subject of a running joke on the comedy show, now in its 31st season, can simultaneously house a wisecracking... 7
8 C O M E D Y J O K E O N T H E C O M E D Y 8
9 C O M E D Y J O K E O N T H E C O M E D Y 9
10 C J J O M E D Y O K E O N T H E C O M E D Y 10
11 C O M E D Y J O K E O N T H E C O M E D Y 11
12 C O O M E D Y J O K E O N T H E C O M E D Y 12
13 C O M E D Y J O K E O N T H E C O M E D Y 13
14 C K O M E D Y J O K E O N T H E C O M E D Y 14
15 C O M E D Y J O K E O N T H E C O M E D Y 15
16 C O M E D Y J O K E O N T H E C O M E D Y 16
17 C O M E D Y J O K E O N T H E C O M E D Y 17
18 J O K E O N T H E C O M E D Y C O M E D Y C O M E D Y 18
19 C O M E D Y J O K E O N T H E C O M E D Y 19
20 C O M E D Y J O K E O N T H E C O M E D Y 20
21 C O M E D Y O J O K E O N T H E C O M E D Y 21
22 C O M E D Y O J O K E O N T H E C O M E D Y 22
23 C O M E D Y J O K E O N T H E C O M E D Y 23
24 C O M E D Y H J O K E O N T H E C O M E D Y 24
25 H C O M E D Y J O K E O N T H E C O M E D Y 25
26 C O M E D Y J O K E O N T H E C O M E D Y 26
27 C O M E D Y E J O K E O N T H E C O M E D Y 27
28 C O M E D Y E J O K E O N T H E C O M E D Y 28
29 C O M E D Y J O K E O N T H E C O M E D Y 29
30 C O M E D Y C O M E D Y J O K E O N T H E C O M E D Y Key Property: The longer the pattern, the faster the search! 30
31 Pre-Computing the Skip Distance pat: COMEDY txt: xxxxxoxxxxxxxxxxx... A 6 F 6 K 6 P 6 U 6 B 6 G 6 L 6 Q 6 V 6 C 5 H 6 M 3 R 6 W 6 D 1 I 6 N 6 S 6 X 6 E 2 J 6 O 4 T 6 Y 0 Z 6 This is a 1-dimensional array, skip[c], as big as the alphabet. 31
32 C O M E D Y J O K E O N T H E C O M E D Y skip[c]: A 6 F 6 K 6 P 6 U 6 B 6 G 6 L 6 Q 6 V 6 C 5 H 6 M 3 R 6 W 6 D 1 I 6 N 6 S 6 X 6 E 2 J 6 O 4 T 6 Y 0 Z 6 32
33 C O M E D Y J O K E O N T H E C O M E D Y skip[c]: A 6 F 6 K 6 P 6 U 6 B 6 G 6 L 6 Q 6 V 6 C 5 H 6 M 3 R 6 W 6 D 1 I 6 N 6 S 6 X 6 E 2 J 6 O 4 T 6 Y 0 Z 6 33
34 C O M E D Y O J O K E O N T H E C O M E D Y skip[c]: A 6 F 6 K 6 P 6 U 6 B 6 G 6 L 6 Q 6 V 6 C 5 H 6 M 3 R 6 W 6 D 1 I 6 N 6 S 6 X 6 E 2 J 6 O 4 T 6 Y 0 Z 6 34
35 C O M E D Y O J O K E O N T H E C O M E D Y skip[c]: A 6 F 6 K 6 P 6 U 6 B 6 G 6 L 6 Q 6 V 6 C 5 H 6 M 3 R 6 W 6 D 1 I 6 N 6 S 6 X 6 E 2 J 6 O 4 T 6 Y 0 Z 6 35
36 C O M E D Y J O K E O N T H E C O M E D Y skip[c]: A 6 F 6 K 6 P 6 U 6 B 6 G 6 L 6 Q 6 V 6 C 5 H 6 M 3 R 6 W 6 D 1 I 6 N 6 S 6 X 6 E 2 J 6 O 4 T 6 Y 0 Z 6 36
37 C O M E D Y H J O K E O N T H E C O M E D Y skip[c]: A 6 F 6 K 6 P 6 U 6 B 6 G 6 L 6 Q 6 V 6 C 5 H 6 M 3 R 6 W 6 D 1 I 6 N 6 S 6 X 6 E 2 J 6 O 4 T 6 Y 0 Z 6 37
38 H C O M E D Y J O K E O N T H E C O M E D Y skip[c]: A 6 F 6 K 6 P 6 U 6 B 6 G 6 L 6 Q 6 V 6 C 5 H 6 M 3 R 6 W 6 D 1 I 6 N 6 S 6 X 6 E 2 J 6 O 4 T 6 Y 0 Z 6 38
39 C O M E D Y J O K E O N T H E C O M E D Y skip[c]: A 6 F 6 K 6 P 6 U 6 B 6 G 6 L 6 Q 6 V 6 C 5 H 6 M 3 R 6 W 6 D 1 I 6 N 6 S 6 X 6 E 2 J 6 O 4 T 6 Y 0 Z 6 39
40 C O M E D Y E J O K E O N T H E C O M E D Y skip[c]: A 6 F 6 K 6 P 6 U 6 B 6 G 6 L 6 Q 6 V 6 C 5 H 6 M 3 R 6 W 6 D 1 I 6 N 6 S 6 X 6 E 2 J 6 O 4 T 6 Y 0 Z 6 40
41 C O M E D Y E J O K E O N T H E C O M E D Y skip[c]: A 6 F 6 K 6 P 6 U 6 B 6 G 6 L 6 Q 6 V 6 C 5 H 6 M 3 R 6 W 6 D 1 I 6 N 6 S 6 X 6 E 2 J 6 O 4 T 6 Y 0 Z 6 41
42 C O M E D Y J O K E O N T H E C O M E D Y skip[c]: A 6 F 6 K 6 P 6 U 6 B 6 G 6 L 6 Q 6 V 6 C 5 H 6 M 3 R 6 W 6 D 1 I 6 N 6 S 6 X 6 E 2 J 6 O 4 T 6 Y 0 Z 6 42
43 C O M E D Y C O M E D Y J O K E O N T H E C O M E D Y skip[c]: A 6 F 6 K 6 P 6 U 6 B 6 G 6 L 6 Q 6 V 6 C 5 H 6 M 3 R 6 W 6 D 1 I 6 N 6 S 6 X 6 E 2 J 6 O 4 T 6 Y 0 Z 6 43
44 But Wait! There s More! pat: NONPARTIPULAR txt:
45 But Wait! There s More! pat: NONPARTIPULAR txt: R
46 But Wait! There s More! pat: NONPARTIPULAR txt: A
47 But Wait! There s More! pat: NONPARTIPULAR txt: P
48 But Wait! There s More! pat: NONPARTIPULAR txt: P Slide 2 to match the discovered character. 48
49 But Wait! There s More! pat: NONPARTIPULAR txt: P??
50 But Wait! There s More! pat: NONPARTIPULAR txt: PAR
51 But Wait! There s More! pat: NONPARTIPULAR txt:
52 But Wait! There s More! pat: NONPARTIPULAR txt: R
53 But Wait! There s More! pat: NONPARTIPULAR txt: AR
54 But Wait! There s More! pat: NONPARTIPULAR txt: PAR
55 But Wait! There s More! pat: NONPARTIPULAR txt: PAR
56 But Wait! There s More! pat: NONPARTIPULAR txt: PAR Slide 7 to match the discovered substring! 56
57 j pat pat: NONPARTIPULAR txt: PAR i dt: txt[i] pat[j + 1]... pat[ pat ] P A R 57
58 dt: txt[i] pat[j + 1]... pat[ pat ] dt can be computed given txt[i] and index j in pat! There are only α pat combinations, where α is the alphabet size. 58
59 The Skip Distance Delta Given pat, the skip can be pre-computed for every combination of character read, c, and pattern index, j, by finding how far we must slide to find the last occurrence of dt in pat. 59
60 pat: NONPARTIPULAR txt: PAR
61 pat: NONPARTIPULAR txt: PAR
62 pat: BC-ABC-BBC-CBC txt: BBC
63 pat: BC-ABC-BBC-CBC txt: BBC
64 pat: BC-ABC-BBC-CBC txt: ABC
65 pat: BC-ABC-BBC-CBC txt: ABC
66 pat: BC-ABC-BBC-CBC txt: DBC
67 pat: BC-ABC-BBC-CBC txt: DBC
68 pat: EE-ABC-BBC-CBC txt: DBC
69 pat: EE-ABC-BBC-CBC txt: DBC
70 The Delta Array delta[c,j] is an array of size α pat that gives the skip distance when a mismatch occurs after comparing c from txt to pat[j]. 70
71 The Algorithm fast(pat, txt) If pat = "" then If txt = "" then return Not-Found; else return 0; end; end; 71
72 preprocess pat to produce delta; j := pat 1; i := j; 72
73 while (0 j i < txt ) do If pat[j] = txt[i] then i := i 1; j := j 1; else i := i + delta[txt[i],j]; j := pat 1; end; 73
74 If (j < 0) then return i + 1; else return Not-Found; end; end; 74
75 Performance How does the algorithm perform? This depends on the size of the alphabet. We only have data on English text right now. In our test: txt: English text of length 177,
76 pat: 100 randomly chosen patterns of length 5 30, chosen from another English text and filtered so they do not occur in the search text. The naive string searching algorithm would look at all 177,985 characters of the search text. In fact, it would look at some characters more than once. 76
77 77
78 78
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