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Variations of Forward-SBNDM

Variations of Forward-SBNDM. Hannu Peltola Jorma Tarhio Aalto University Finland. Aims. Tuning algorithms for exact string matching. Studying the effect of simultaneous 2-byte read. SBNDM Simple Backward Nondeterministic DAWG Matching.

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Variations of Forward-SBNDM

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  1. Variations of Forward-SBNDM Hannu Peltola Jorma Tarhio Aalto University Finland

  2. Aims • Tuning algorithms for exact string matching. • Studying the effect of simultaneous 2-byte read. Aug. 29, 2011

  3. SBNDMSimple Backward Nondeterministic DAWG Matching • SBNDM [18] is a simplification of BNDM [17].Both are bit-parallel algorithms. • Text T = t1...tn, pattern P = p1...pm. • At each alignment window of P in T, scan T from right to left until the suffix of the window is not a factor of P or an occurrence of P is found. Aug. 29, 2011

  4. Shift of SBNDM • No factor: m • P found: 1 • Else: next alignment starts at the last factor Aug. 29, 2011

  5. SBNDM, example P = banana, T = antanabadbanana...alignment: antanabadbananaa na ana Aug. 29, 2011

  6. SBNDM, example P = banana, T = antanabadbanana...alignment: antanabadbananaa na ananot a factor: tananext alignment: antanabadbanana Aug. 29, 2011

  7. SBNDM, example P = banana, T = antanabadbanana...alignment: antanabadbanana a na ananot a factor:tananext alignment: antanabadbanana not a factor:dnext alignment:antanabadbanana Aug. 29, 2011

  8. SBNDMq • SBNDMq [6] is a tuned version of SBNDM. • Processing of an alignment starts with checking a q-gram. • Let q = 4. Consider an alignment at antana. Instead of testing four suffixes a, na, ana, tana,only tana is tested. • Testing is done in a fast loop. Aug. 29, 2011

  9. Forward-SBNDM • Forward-SBNDM (FSB for short) by Faro & Lecroq [7] is a lookahead version of SBNDM2. • Both FSB and SBNDM2 read a 2-gram x1x2 before a factor test. • x1x2 is matched with the end of P in SBNDM2. • Only x1 is matched with the end of P in FSB, and x2 is a lookahead character following the current alignment. • FSB is faster than SBNDM2 for large alphabets. Aug. 29, 2011

  10. Generalization of FSB: FSB(q,f) • FSB(q,f) (= Forward-SBNDM(q,f)) is SBNDMq with f lookahead characters, f = 0, 1, ..., q-1. • FSB(2,1) = FSB and FSB(q,0) = SBNDMq. • Motivation: SBNDMq works well on modern processors also for q>2. Aug. 29, 2011

  11. FSB(q,f) • Let UV be a q-gram, where |V| = f. • Afterreading UV there are 3 alternatives: • If U is a suffix of P, reading continues leftwards. • Else if UV is a factor of P, reading continues leftwards. • Else the state vector is zero and P is shifted m-q+f+1 positions (f positions more than in SBNDMq). Aug. 29, 2011

  12. Occurrence vectors in FSB(q,2) • Example: P = banana bananaSBNDMq: B[n] = 00001010FSB(q,2): B[n] = 00101011 B[a] = 01010111B[x] = 00000011 extra bits Aug. 29, 2011

  13. State vectors in FSB(q,2) for q=4 4-gram nanx: x 00000011 n 00101011 a 01010111n 00101011 00001000 4-gram State vector Conclusionnanx00001000 na is a suffix of Pxana00000000not a factoranan01000000 factor of P nanx is not a factor Aug. 29, 2011

  14. Benefits / drawbacks of lookahead characters and extra bits • Benefits • Longer shifts  more speed • Combined suffix/factor test • Drawback • More q-grams accepted  less speed Aug. 29, 2011

  15. Greedy skip loop for SBNDM2 (GSB2 = Greedy-SBNDM2) • Factor tests of two 2-grams are done in one round. • Let B2[x,y] denote the combined occurrence vector of characters x and y. B2[x,y] = B[x] & (B[y]<<1) next: D  B2[ti,ti+1] if D = 0 then if B2[ti+m-1,ti+m] = 0 then i  i+2*m-2 goto next Aug. 29, 2011

  16. 2-byte read • Read two characters (= 2 bytes = 16 bits) in one instruction (in a skip loop). • Suits well q-gram algorithms with even q. • For experiments we made two versions of the algorithms: • Standard (1-byte read) • b-version using 2-byte read Aug. 29, 2011

  17. 2-byte read (cont.) • Advantage: a part of computation can moved to preprocessing phase • Example: B2[x,y] = B[x] & (B[y]<<1) • Speed-up factor even more than 2 • Drawback: extra 0.1 ms for preprocessing. Aug. 29, 2011

  18. 4-byte read? • Many border crosses happen => slow down • 232 tables too big for practice Aug. 29, 2011

  19. Experimental results/KJV Bible • In the recent comparison S. Faro, T. Lecroq: The Exact String Matching Problem: a Comprehensive Experimental Evaluation (2010), the algorithms EBOM and Hash3 were the fastest in the bible text for m = 4,...,20. Aug. 29, 2011

  20. KJV: EBOM & Hash3 (on ThinkPad X61s) Aug. 29, 2011

  21. KJV: EBOMb & Hash3b (with 2-byte read) added Aug. 29, 2011

  22. KJV: SBNDM2b = FSB(2,0)b added Aug. 29, 2011

  23. KJV: GSB2b added Aug. 29, 2011

  24. KJV: FSB(4,i)b added, i = 0,1,2 Aug. 29, 2011

  25. KJV: Speed-up factors of 2-byte read GSB2 1.32 FSB(2,0) 1.34 FSB(2,1) 1.24 FSB(4,0) 1.72 FSB(4,1) 2.15 FSB(4,2) 2.03 Hash3 1.05 EBOM 1.17 Aug. 29, 2011

  26. Other experiments • DNA and binary data was also tested. • Gain of lookahead characters or the greedy loop was smaller than with the bible data. • Gain of 2-byte read was smaller with 64-bit code than with 32-bit code. Aug. 29, 2011

  27. Conclusions • Two new algorithms were presented: • FSB(q,f) • GSB2 • The new algorithms are faster than earlier algorithms on English data: • GSB2 for m = 4, …, 8 • FSB(q,f) for m = 8, …, 20 • 2-byte read makes most string algorithms faster. Aug. 29, 2011

  28. Web site for practical speed comparison cse.aalto.fi/stringmatching Aug. 29, 2011

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