Character Matching

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Character Matching

• Systolic Design Character Matching
• A straightforward approach to search for a
  pattern within a string of characters (string) is
  simple but time-consuming.
• The following algorithm shows the sequence of
  operations.
• The algorithm compares the characters in the
  pattern against the characters in the text from
  left to right.
• This simple algorithm has a time complexity of
  O(mn) where m and n are the lengths of the
  pattern and text.

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Systolic Design Character Matching

• Search for a Pattern

T-index ? 0 While T-index lt (n-m1) DO Save ?
T-index P-index ? 0 While P-index lt m and
Textsave PatternP-index DO Save ? Save
1 P-index ? P-index 1 END If P-index m
then return T-index ? T-index 1 END
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Systolic Design Character Matching

• Concept of the finite state automaton can be used
  to perform pattern matching operation in a time
  complexity of O(n).
• Knuth proposed an algorithm with the time
  complexity of O(mn).

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Systolic Design Character Matching

• The proposed model is used for character matching
  (pattern Matching) operation.
• The model is composed of two kind of cells
• Comparator cells, and
• Accumulator cells.

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Systolic Design Character Matching

• The comparator cells receive text and patterns
  from opposite directions and generate the
  Comparison results.
• The accumulator cells transmit information
  regarding delimiters and "don't care" signals.
  In addition, it accumulates the partial match
  results.

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• Systolic Design Character Matching

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Systolic Design Character Matching

• Algorithm in C cells

Pout ? Pin Sout ? Sin dout ? (Pin Sin)
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Systolic Design Character Matching

• Algorithm in A cells

lout ? lin Xout ? Xin IF lin THEN rout ? t t ?
True ELSE rout ? rin t ? t AND (Xin OR din)
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Systolic Design Character Matching

• Detect pattern ISSI in text MISSISSIPPI in a
  systolic organization composed of seven cells.

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Systolic Design Character Matching

• Initial configuration

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Systolic Design Character Matching
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Systolic Design Character Matching
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Systolic Design Character Matching
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Systolic Design Character Matching
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Systolic Design Character Matching
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Systolic Design Character Matching
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Systolic Design Character Matching

• General Characteristics
• Hardware utilization is low, since during each
  clock pulse only half of the cells are active.
• Patterns have to be cycled through the array
  continuously to meet all the text characters.
• Possible detection of more hits in the input text.

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Systolic Design Join Operation

• Within the scope of relational databases, join is
  one of the most time consuming operations.

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Systolic Organization

• Assume we have two product-compatible relations
  (sets) A and B. Each relation is composed of
  several tuples (records).
• Further, let ? ???, ?, ?, ...?, then the ?-Join
  of relation A on attribute X with relation B on
  attribute Y is a relation consist of tuples
  t(lta,bgt) from Cartesian product of A and B such
  that tx ? ty is true.

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Systolic Design Join Operation

• Assume we have the following two relations

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Systolic Design Join Operation
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Systolic Design Join Operation

• In relational database system, join operation is
  used as a measure to evaluate the performance of
  the system.
• This is due to the
• Complexity of the join, and
• application of join in de-normalizing the
  relations.

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Systolic Design Join Operation

• Let us look at a systolic model for join
  operation
• A collection of basic cells replicated in a two
  dimensional space.
• System is highly parallel and satisfies the
  constraints imposed by the VLSI technology.

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Systolic Design Join Operation

• A Systolic Cell

as and bs are the attributes and t is a control
signal that reflects the comparison between a and
b.
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Systolic Design Join Operation

• A Systolic Cell

Tout ? tin ? (ain ? bin) aout ? ain bout ? bin
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Systolic Design Join Operation
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Systolic Design Join Operation
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Systolic Design Join Operation
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Systolic Design Join Operation
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• Systolic Design Join Operation

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Systolic Design Join Operation
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Systolic Design Join Operation