Parallel%20String%20Matching%20Algorithm(s)%20Using%20Associative%20Processors

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Parallel String Matching Algorithm(s) Using
Associative Processors

• Original work by
• Mary Esenwein and Dr. Johnnie Baker
• Presented by Shannon Steinfadt
• April 18, 2007

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String Matching Problem

• Aka. pattern matching or string searching
• Useful in many applications such as text editing
  and information retrieval, DNA analysis, Homeland
  Security

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What are we doing?

• Given a pattern and some text, find out if the
  pattern is IN the text
• Is pattern AB in the text ABAA? If so, where?

AB
ABAA
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Whats the notation?

• P is a pattern string of length m
• T is a text string of length n, usually n m

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Goal of String Matching

• To find all occurrences of a pattern string in
  the text string
• Locate all positions i in T such that Tij-1
  Pj for all j, 1 j m

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Pattern Variations

• An exact pattern
• A Dont Care character () in pattern
• Flexibility in matching
• indicates character(s) of the text that are
  irrelevant to the matching process

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General Dont Care Characters ()
Characteristics

• Single character of text
• Multiple consecutive text characters
• No characters
• Combination of above three
• Example
• Pattern ABCD could match ABBCD, ABBBBBCD, or
  ABCD ( is null)

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String Matching using ASC

• Three parallel algorithms using associative
  computing (using 1-D mesh)
• String matching for exact match
• String matching with fixed length dont care
• I.e., exactly 1 character
• String matching with variable length dont care
• a dont care can have any length or be null

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ASC Exact Match Algorithm

• for (j patt_length - 1 j gt 0 j--)
• Responders are text patt_stringj
• and counter patt_counter
• Responders add 1 to counter and store
  result in counter of preceding cell
• patt_counter
• / When pattern has been processed /
• Responders are counter patt_length
• Responders set match 1 in next cell

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Text
Match
Counter
_at_ 0 0
A 0 0
B 0 0
B 0 0
B 0 0
A 0 0
B 0 0
B 0 0
B 0 0
A 0 0
B 0 0
A 0 0
Pattern BBA Text ABBBABBBABA mpattern
length ntext length j pattern index i text
index
Pattern BBA
patt_ counter
0
patt_length
3
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(No Transcript)
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Text Match Counter
Final State of Exact Match Algorithm
_at_ 0 1
A 0 0
B 0 3
B 1 2
B 0 1
A 0 0
B 0 3
B 1 2
B 0 1
A 0 2
B 0 1
A 0 0
Pattern BBA Text ABBBABBBABA m pattern
length n text length j pattern index i text
index
B
B
A
1
0
0
1
0
0
B
B
A
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Algorithm for unit length "don't cares" using ASC

• for (j patt_length - 1 j gt 0 j--)
• if (patternj '')
• Responders are counter patt_counter
• else // patternj is not the dont care
  character
• Responders are text patternj
• and counter patt_counter
• If no Responders are detected, exit
• Responders add 1 to counter and store result
  in counter of preceding cell
• patt_counter
• / When pattern has been processed /
• Responders are counter patt_length
• Responders set match 1 in next cell

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ASC Exact Match Algorithm (again)

• for (j patt_length - 1 j gt 0 j--)
• Responders are text patt_stringj
• and counter patt_counter
• Responders add 1 to counter and store
  result in counter of preceding cell
• patt_counter
• / When pattern has been processed /
• Responders are counter patt_length
• Responders set match 1 in next cell

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Text
Match
Counter
_at_ 0 0
A 0 0
B 0 0
B 0 0
B 0 0
A 0 0
B 0 0
B 0 0
B 0 0
A 0 0
B 0 0
A 0 0
Pattern BBA Text ABBBABBBABA mpattern
length ntext length j pattern index i text
index
Pattern BA
patt_ counter
0
patt_length
3
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(No Transcript)
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Text Match Counter
Final State of Exact Match Algorithm
_at_ 0 1
A 0 0
B 0 3
B 1 2
B 0 1
A 0 0
B 0 3
B 1 2
B 0 1
A 0 2
B 0 1
A 0 0
Pattern BA Text ABBBABBBABA m pattern
length n text length j pattern index i text
index
B
B
A
1
0
0
1
0
0
B
B
A
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VLDC Algorithm (added)

• Works on each segment of the pattern broken up
  by the character
• ABBBA has three sections
• Consecutive characters not necessary, not
  allowed
• This VLDC algorithm unique
• Provides information to find all continuation
  points of all matches following each

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VLDC ALGORITHM USING ASC

• int patt_length m
• int maxcell n 2
• / Special handling for at end of pattern /
• if (patternm-1 )
• Responders are cell index gt 1
• Responders set segment0 1
• patt_counter 1
• k 1 / Reset initial segment index /
• while ((patt_length - patt_counter) gt 0
  maxcell gt 0)
• patt_counter 0
• for ( I patt_length - 1 Igt 0 patternI
  ! I--)
• Responders are text patternI and counter
  patt_counter and cell index lt maxcell
• Responders add 1 to counter and store result
  in counter of preceding cell
• patt_counter

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VLDC continued

• Responders set segmentk patt_counter in next
  cell
• Responders are segmentk gt 0
• maxcell maximum cell index value of Responders
  
• else if no Responders maxcell 0
• All cells become Responders and set counter
  0
• patt_counter k
• / When pattern has been processed /
• Responders are segment--k gt 0
• Responders set match 1
• / Special handling for at start of pattern
  /
• if (pattern0 )
• Responders are cell index lt maxcell and cell
  index gt 1
• Responders set match 1

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After third pattern segment in VLDC Algorithm
Pattern ABBBA Text ABBBABBBABA
T
M
C
S0
S1
S2
Responder
_at_ 0 0 ?1?0 0 0 0 Y ? N
A 0 0 0?1 0 0 Y
B 0 0 0 0 0
B 0 0 0 0 0
B 0 0 ?1?0 0 0 0 Y ? N
A 0 0 0?1 0 0 Y
B 0 0 0 0 0
B 0 0 0 0 0
B 0 0 ?1?0 0 0 0 Y ? N
A 0 0 0?1 0 0 Y
B 0 0 ?1?0 0 0 0 Y ? N
A 0 0 0?1 0 0 Y
1
2
Patt_counter
3
4
0?1 ?2
5
6
7
Maxcell
8
13?12
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10
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After second pattern segment in VLDC Algorithm
Pattern ABBBA Text ABBBABBBABA
T
M
Counter
S0
S1
S2
Responder
_at_ 0 0 0 0 0
A 0 0 ?1 ?2 ?0 1 0 0 Y
B 0 0 ?1 ?2 ?0 0 0 ?2 0 Y ?Y ?Y
B 0 0 ?1 ?0 0 0 ?2 0 Y ?Y ?N
B 0 0 0 0 0 Y ?N
A 0 0 ?1 ?2 ?0 1 0 0 Y
B 0 0 ?1 ?2 ?0 0 0 ?2 0 Y ?Y ?Y
B 0 0 ?1 ?0 0 0 ?2 0 Y ?Y ?N
B 0 0 0 0 0 Y ?N
A 0 0 ?1?0 1 0 0
B 0 0 0 0 0 Y ?N
A 0 0 1 0 0
1
2
Patt_counter
3
4
0?1?2 0?1?2?3
5
6
7
Maxcell
8
13?12 ?8
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10
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(Used to keep pattern segments in order, I.e. AB
occurs before BB)
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After first pattern segment in VLDC Algorithm
Pattern ABBBA Text ABBBABBBABA
T
M
Counter
S0
S1
S2
Responder
_at_ 0 0 ?2 ?0 0 0 0 Y
A 0 0 ?1 ?0 1 0 0?2 Y ? N
B 0 0 ?1 ?0 0 2 0 Y ? N
B 0 0 ?1 ?0 0 2 0 Y ? N
B 0 0 ?2 ?0 0 0 0 Y ? N ? Y
A 0 0 ?1 ?0 1 0 0?2 Y ? N
B 0 0 0 2 0 Y ? N
B 0 0 0 2 0
B 0 0 0 0 0
A 0 0 1 0 0
B 0 0 0 0 0
A 0 0 1 0 0
1
2
Patt_counter
3
4
0?1?2 0?1?2?3 0?1?2?3
5
6
7
Maxcell
8
13?12 ?8 ?6
9
10
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(Used to keep pattern segments in order, I.e. AB
occurs before BB)
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Final State in VLDC Algorithm
Pattern ABBBA Text ABBBABBBABA
T
M
Counter
S0
S1
S2
Responder
_at_ 0 0 0 0 0
A 1 0 1 0 2 Y
B 0 0 0 2 0
B 0 0 0 2 0
B 0 0 0 0 0
A 1 0 1 0 2 Y
B 0 0 0 2 0
B 0 0 0 2 0
B 0 0 0 0 0
A 0 0 1 0 0
B 0 0 0 0 0
A 0 0 1 0 0
1
2
Patt_counter
3
4
0?1?2 0?1?2?3 0?1?2?3
5
6
7
Maxcell
8
13?12 ?8 ?6
9
10
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(Used to keep pattern segments in order, I.e. AB
occurs before BB)
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Finding All Continuation Points

• Match starts where M 1
• Match to any pattern segment begins where Sx
  segment length
• i.e. where any Sx gt 0
• Continuation of match in Sx-1 whose cell/PE
  index is gt (Sx segment size) of Sxs
  cell/PE index

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Using the Final State in VLDC Algorithm
Pattern ABBBA Text ABBBABBBABA
S0
S1
S2
T
M
C
_at_ 0 0 0 0 0
A 1 0 1 0 2
B 0 0 0 2 0
B 0 0 0 2 0
B 0 0 0 0 0
A 1 0 1 0 2
B 0 0 0 2 0
B 0 0 0 2 0
B 0 0 0 0 0
A 0 0 1 0 0
B 0 0 0 0 0
A 0 0 1 0 0

• Start with index 2, where theres a match M1
• Work from S2 down and left, count down 2 values
  and move into S1, count down 2 values and move
  to S0
• That produces 2?4?6 ABBBA
• Any index gt 4 in S1 whose value is gt0 will
  also produce a correct match
• 2?7?10 ABBBABBBA
• 2?8?10 ABBBABBBA
• Some of the additional matches are
• 2?4?10 ABBBABBBA
• 2?4?12 ABBBABBBABA
• 2?8?12 ABBBABBBABA
• 6?8?10 ABBBA
• 6?8?12 ABBBABA

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Existing Algorithms

• Sequential Algorithms
• Naïve algorithm O(mn)
• Knuth, Morris, Pratt, or Boyer-Moore O(mn)
• Parallel Algorithms
• A PRAM exact string matching O(n)
• On a reconfigurable mesh O(1) on n(n-m1) PEs
• On a SIMD hypercube (limited to 0,1) O(lg n)
  on n/lg n PEs
• On a neural network O(1) on nm PEs
• ASC algorithms O(m) time on O(n) PEs

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Question to consider

• The dont care character allows non-matching
  for an arbitrary length. This is discussed on
  slide 13. Instead, consider to allow a
  non-match for two characters and make necessary
  changes in trace in Slide 15-16.