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String Matching of Bit Parallel Suffix Automata

String Matching of Bit Parallel Suffix Automata. Suffix Automata. Base on a Deterministic Acyclic Word Graph (DAWG) To facilitate comparing equivalence suffix string Nondeterministic suffix automata Deterministic suffix automata. Subset Construction.

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String Matching of Bit Parallel Suffix Automata

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  1. String Matching of Bit Parallel Suffix Automata

  2. Suffix Automata • Base on a Deterministic Acyclic Word Graph (DAWG) • To facilitate comparing equivalence suffix string • Nondeterministic suffix automata • Deterministic suffix automata Subset Construction

  3. Also called Backward Deterministic automata Matching (BDM) Build the factor x for pattern p endpos(x) set of all the pattern position where an occurrence of x ends Ex: Pattern = baabbaa, endpos(aa) = {3,7} Safe shift, if no equivalent suffix in pattern Suffix Automata Search Text: shift left to right Windows size = pattern length Fail to matching a factor Shift window

  4. BDM Algorithm Build automata Reached the final state

  5. Suffix Automata Search Example 1. Build Reverse Deterministic Suffix Automata 2. endpos(x) to find a factor 3. Fail to find a factor, do a safe shift

  6. Suffix Automata Search Example 1. T= [abbaba a ]bbaab a is a factor of pr and a reverse prefix of p. last =6 2367 b a 6 a a 01234567 26 7 37 4 a a a b b b 145 5 b

  7. Suffix Automata Search Example 2. T= [abbab aa ]bbaab aa is a factor of pr and a reverse prefix of p. last =5 2367 b a 6 a a 01234567 26 7 37 4 a a a b b b 145 5 b

  8. Suffix Automata Search Example 3. T= [abba baa ]bbaab aab is a factor of pr 2367 b a 6 a a 01234567 26 7 37 4 a a a b b b 145 5 b

  9. Suffix Automata Search Example 4. T= [abb abaa ]bbaab We fail to recognize the next a.So we shift the window to last. We search again in position:T= abbab[aabbaab] . last=7 2367 b a 6 a a 01234567 26 7 37 4 a a a b b b 145 5 b

  10. Suffix Automata Search Example 5. T= abbab[aabbaa b ] b is a factor of pr 2367 b a 6 a a 01234567 26 7 37 4 a a a b b b 145 5 b

  11. Suffix Automata Search Example 6. T= abbab[aabba ab ] ba is a factor of pr 2367 b a 6 a a 01234567 26 7 37 4 a a a b b b 145 5 b

  12. Suffix Automata Search Example 7. T= abbab[aabb aab ] baa is a factor of pr and a reverse prefix of p. last =4 2367 b a 6 a a 01234567 26 7 37 4 a a a b b b 145 5 b

  13. Suffix Automata Search Example 8. T= abbab[aab baab ] baab is a factor of pr 2367 b a 6 a a 01234567 26 7 37 4 a a a b b b 145 5 b

  14. Suffix Automata Search Example 9. T= abbab[aa bbaab ] baabb is a factor of pr 2367 b a 6 a a 01234567 26 7 37 4 a a a b b b 145 5 b

  15. Suffix Automata Search Example 10. T= abbab[a abbaab ] baabba is a factor of pr 2367 b a 6 a a 01234567 26 7 37 4 a a a b b b 145 5 b

  16. Suffix Automata Search Example 11. T= abbab[ aabbaab ] We recognize the word aabbaab and report an occurrence. 2367 b a 6 a a 01234567 26 7 37 4 a a a b b b 145 5 b

  17. BNDM Algorithm • Backward Nondeterministic Dawg Matching (BNDM) • Handle class, multiple pattern, and allow errors • Using bit parallelism, Combine Shift-Or and BDM • Faster than BDM 20% ~ 25%, Faster than BM 10% ~ 40% • Update Function

  18. BNDM Algorithm

  19. BNDM Example

  20. BNDM Example

  21. BNDM Further Improvement • Handle long pattern • Partition pattern p into subpatterns pi • Build a array of D and B, process each part with basic algorithm • If pi is found, than process pi+1 … • Handle Class • Modified B table only • Have the ith bit set for all chars belonging to ith position in pattern • Multiple Pattern • Two method • Interleave patterns, shift r bit for each D update • Just concatenate, shift 1 bit, but modifed D = (D<<1) &(1m-10)r • Where r is # of patterns • Approximate Matching • Use Wu’s method

  22. Performance Comparison In 1/100 of second per megabyte

  23. Reference • Gonzalo Navarro and Mathieu Raffinot. A Bit-parallel approach to Suffix Automata: Fast Extended String Matching. In M. Farach (editor), Proc. CPM'98, LNCS 1448. Pages 14-33, 1998. • Gonzalo Navarro, Mathieu Raffinot, Fast and Flexible String Matching by Combining Bit-parallelism and Suffix Automata (1998)

  24. Rreverse Pattern ?

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