A Multiple Sliding Windows Approach to Speed Up String Matching Algorithms
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1 A Multiple Sliding Windows Approach to Speed Up String Matching Algorithms Simone Faro Thierry Lecroq University of Catania, Italy University of Rouen, LITIS EA 4108, France Symposium on Eperimental Algorithms June 7th-9th 2012 Bordeau, France
2 Outline 1 Introduction to eact string matching 2 Classical solutions 3 New solutions 4 Eperimental results SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
3 Outline 1 Introduction to eact string matching 2 Classical solutions 3 New solutions 4 Eperimental results SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
4 Eact String Matching Definition Find all the occurrences of a pattern of length m in a tet y of length n., y Σ 2 instances is given first y is given first SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
5 Eact String Matching Interests basic components of many softwares theoretical problems SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
6 Eact String Matching Theory linear time since Morris and Pratt 1970 linear time and constant space O((n log m)/m) in average [Yao 1979] SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
7 Eact String Matching Solutions Many!! see SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
8 Efficient solutions S. Faro and T. Lecroq The Eact Online String Matching Problem: a Review of the Most Recent Results ACM Computing Surveys 45(2) (2013) to appear. SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
9 Outline 1 Introduction to eact string matching 2 Classical solutions 3 New solutions 4 Eperimental results SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
10 Eact String Matching Classical solutions comparisons Knuth-Morris-Pratt (KMP) Boyer-Moore (BM) automata Backward DAWG Matching (with suffi automaton or oracle) (BDM) bit-parallelism Shift Or (SO) Backward Nondeterministic DAWG Matching (BNDM) filtering Karp-Rabin (KR) SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
11 Sliding Window y window beginning SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
12 Sliding Window y window middle SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
13 Sliding Window y window middle SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
14 Sliding Window y window end SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
15 Boyer-Moore (1977) y SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
16 Boyer-Moore (1977) y comparisons b v = a v SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
17 Boyer-Moore (1977) y comparisons b v = a v = c v good suffi shift (1) SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
18 Boyer-Moore (1977) y comparisons b v = a v = good suffi shift (2) v SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
19 Boyer-Moore (1977) y comparisons b v = a v bad character shift b no b SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
20 Fast Search (Cantone-Faro, 2003) uses the bad character shift when a mismatch occurs with the pattern righmost character uses the good suffi shift otherwise SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
21 TVSBS (Thathoo-Virmani-Lakshmi-Balakrishnan-Sekar, 2006) compares first the rightmost character of the window then the leftmost, then all the others uses both the righmost character of the window and the following to perform the shift SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
22 TVSBS (Thathoo-Virmani-Lakshmi-Balakrishnan-Sekar, 2006) y SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
23 TVSBS (Thathoo-Virmani-Lakshmi-Balakrishnan-Sekar, 2006) y a = a SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
24 TVSBS (Thathoo-Virmani-Lakshmi-Balakrishnan-Sekar, 2006) y b = b a = a SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
25 TVSBS (Thathoo-Virmani-Lakshmi-Balakrishnan-Sekar, 2006) y b = b comparisons u = u c d a = a SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
26 TVSBS (Thathoo-Virmani-Lakshmi-Balakrishnan-Sekar, 2006) forward character comparisons y b = b u = u c d a = a e Berry-Ravindran shift a e no ae SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
27 BNDM (Navarro & Raffinot, 1998) C A T A SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
28 BNDM (Navarro & Raffinot, 1998) C A T A S A S C S G S T SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
29 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
30 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
31 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
32 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T And with S T SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
33 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T And with S T = SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
34 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T And with S T = Shift SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
35 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
36 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T And with S A SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
37 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T And with S A = SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
38 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T And with S A = Shift SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
39 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
40 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T And with S C SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
41 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T And with S C = SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
42 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T And with S C = Shit SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
43 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
44 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T And with S C SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
45 BNDM (Navarro & Raffinot, 1998) C A T A y C C A T A C S A S C S G S T And with S C = SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
46 Outline 1 Introduction to eact string matching 2 Classical solutions 3 New solutions 4 Eperimental results SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
47 Partition the tet in k/2 substrings and use k windows m < n/k and k is even (A) s 0 }{{} w 0 (B) s 0 }{{} { w 1 }} { s 1 w 0 (C) s 0 }{{} w 0 s 1 w 2 {}}{ } {{ } w 1 s 2 { w 3 }} { s 3 A general scheme for the multiple sliding windows matcher with: (A) 1 window (B) 2 windows (C) 4 windows SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
48 A General Multiple Sliding Windows Approach Then process simultaneously the k different tet windows where w 0, w 1,..., w k 1 w 2i = y[(2n/k)i.. (2n/k)i + m 1] and left windows, goes to right w 2i+1 = y[(2n/k)(i + 1) 1.. (2n/k)(i + 1) + m 2] right windows, goes to left for i = 0,..., (k 2)/2 SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
49 Ending situation For each couple of windows (w 2i, w 2i+1 ) the sliding process ends when the window w 2i slides over the window w 2i+1 no occurrence can be missed due to the m 1 overlapping characters between adjacent substrings SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
50 Outline 1 Introduction to eact string matching 2 Classical solutions 3 New solutions 4 Eperimental results SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
51 SMART: String Matching Algorithm Research Tool SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
52 SMART: String Matching Algorithm Research Tool more than 80 string matching algorithms a corpus of 12 tets select/deselect string matching algorithms output eperimental results in L A TEX, ml, html and tt formats easy to plug new algorithms SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
53 Eperiments Random tets of length n = 4, 000, 000 on alphabets of size 16, 32 and 64 for m = 2, 4, 8, 16, 32, 64 with algorithms: Fast Search TVSBS SBNDM FSBNDM and k = 1, 2, 4, 6, 8 windows SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
54 Eperimental results Fast Search TVSBS SBNDM FSBNDM SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
55 Eperiments Random tets of length n = 4, 000, 000 on alphabets of size 16, 32 and 64 for m = 2, 4, 8, 16, 32, 64, 128, 256, 512 and with a protein and a natural language (English) files with algorithms: known EBOM HASH FSBNDM QF new FS-W FSBNDM-W SBNDM-W TVSBS-W SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
56 Eperimental results Alphabet size 32, short patterns SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
57 Eperimental results Alphabet size 32, long patterns SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
58 Eperimental results Protein alphabet (size 20), short patterns SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
59 Eperimental results Protein alphabet (size 20), long patterns SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
60 Eperimental results English tet, short patterns SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
61 Eperimental results English tet, long patterns SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
62 Perspectives implement other known eact string matching algorithms in this multiple window framework truly parallelize apply it to other related problems SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
63 Thank you for your attention! SF&TL (Catania & Rouen) String Matching with Multiple Windows SEA / 34
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