Boyer Moore Searches on Binary Texts

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Boyer Moore Searches on Binary Texts
Accelerating

• Shmuel Tomi Klein
• Miri Kopel Ben-Nissan
• Bar Ilan University, ISRAEL

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Outline
Background and motivation
Boyer Moore algorithm
New binary variant
Analysis
Experiments
Summary
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Important application of Automata
PATTERN MATCHING
KMP BDM BM
Boyer Moore
Match Backwards ! !
this-is-a-sample-text---
pattern
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Boyer Moore Algorithm
Mismatch case 1 delta1
b does not occur in x
y
u
b
x
u
a
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Boyer Moore Algorithm
Mismatch case 2 delta1
b occurs in x
y
u
b
x
u
a
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Boyer Moore Algorithm
Mismatch case 3 delta2
u reoccurs in x preceded by c ? a
y
u
b
x
u
a
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Boyer Moore Algorithm
Mismatch case 4 delta2
Only a suffix v of u reoccurs in x
y
u
b
x
u
a
v
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Boyer Moore Example
rest x p m l e a
7 5 2 3 1 0 4
e l p m a x e
1 7 8 9 10 11 12
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Problems of Binary Boyer Moore
most work by delta1
delta1 useless
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Need for Binary Boyer Moore
Compressed Matching
Given E(T) and P look for
E(P) in E(T)
rather than
P in D(E(T))
Suggested Solution
BBBMM
Blocked Binary Boyer Moore Matching
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BBBMM
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BBBMM
More information in binary case
ffghabdgttiocb sbgghj
ASCII
01100010 01101010
BINARY
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BBBMM
extended delta1
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BBBMM
Total size of delta1 tables
If too large, use limit value
Size of delta1 tables reduced to
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BBBMM
Original delta1 increase of text pointer
BBBMM delta1 shift size
Mismatch not in last block
Correctsh,j
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BBBMM
delta2
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 j
1 0 1 1 0 1 1 1 0 1 0 1 0 1 0 1 Patj
1 2 15 7 3 13 13 13 13 13 13 13 13 13 13 13 delta2j
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Analysis
Assumption random input
Reasonable for compressed text
Expected comparisons till mismatch
Bit-wise
Blocked
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Analysis
Expected bits shifted after mismatch
Bit-wise M
Blocked M
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Experiments
English Bible (2.5MB)
World Factbook (1.5MB)
Text Huffman encoded
k 8
Patterns Random substrings
of lengths 10 to 500
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Experiments
Average comparisons between shifts
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Experiments
Average size of shifts
Bit-wise
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Experiments
Average comparisons for 1000 bits
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Experiments
Time to locate first occurrence (ms)
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Summary
Blocked variant of BM
Faster than alternatives, Overhead 1-10 K
Extensions
ASCII, words instead of characters
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Thank you !