character matching character matching systolic design — character matching a straightforward...

Character MatchingCharacter MatchingSystolic 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(m*n) where m and n are the lengths of the pattern and text.

Systolic Design Systolic Design — Character Matching— Character Matching

Search for a Pattern

T-index 0;While T-index < (n-m+1) DO

Save T-index;P-index 0;While P-index < m and Textsave = PatternP-index DO

Save Save + 1;P-index P-index + 1;

ENDIf P-index = m then return;T-index T-index +1;

END


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(m+n).

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.


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.


C C C C

A A A A•••

••

Pin

Sout

in

Xin

r out

d1 d2 d3 dn

r in

Xout

out

Sin

Pout

tttt

Pattern

String

End ofPattern

Don't Care

Result


Algorithm in C cells:

Pout Pin

Sout Sin

dout (Pin = Sin)


Algorithm in A cells:

out in

Xout Xin

IF in THEN rout t; t True

ELSE rout rin; t t AND (Xin OR din)


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


Initial configuration

IPPISSISSIM

TEXT

ISSI

PATTERN


MI

M

I

M

I

IS

MI

IS


MI

IS

S S

MI

ISS S

MI

ISS

S S I

ISSS S I


ISSIS S I I

Re-circulation

SSI

S I I

SSISS I I S

11

SISI I S


SISSI I S S

II

S SS S

II

SS

SS

II

15

II

SS

S

S


ISSI

SSP

ISI

SP18

IS

SP P I

IP P I


II IPP

I P P


General CharacteristicsGeneral 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.

Systolic Design — Join Operation

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

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(<a,b>) from Cartesian product of A and B such that tx ty is true.

Systolic Organization

A B = a,b a,b A B, and tX tY is true


Assume we have the following two relations:

S# Sname Status CityS1 Smith 20 LondonS2 Jones 10 ParisS3 Blake 30 ParisS4 Clark 20 LondonS5 Adams 30 Athens

SP# Pname Color Weight CityP1 Nut Red 12 LondonP2 Bolt Green 17 ParisP3 Screw Blue 17 RomeP4 Screw Red 14 LondonP5 Cam Blue 12 ParisP6 Cog Red 19 London

P


S# Sname Status S.City P# Pname Color Weight P.CityS1 Smith 20 London P1 Nut Red 12 LondonS1 Smith 20 London P4 Screw Red 14 LondonS1 Smith 20 London P6 Cog Red 19 LondonS2 Jones 10 Paris P2 Bolt Green 17 ParisS2 Jones 10 Paris P5 Cam Blue 12 ParisS3 Blake 30 Paris P2 Bolt Green 17 ParisS3 Blake 30 Paris P5 Cam Blue 12 ParisS4 Clark 20 London P1 Nut Red 12 LondonS4 Clark 20 London P4 Screw Red 14 LondonS4 Clark 20 London P6 Cog Red 19 London

A S.City=P.City B


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.

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.


A Systolic Cella in

t in

b in

b out

t out

a out

a’s and b’s are the attributes andt is a control signal that reflectsthe comparison between a and b.


A Systolic Cell

a in

t in

b in

b out

t out

a out

Tout tin (ain bin)aout ain

bout bin


t41

t14

t13

• • •• • •• • •

Attributes of A relation in

Attributes of B relation in

Elements ofthe Bit Matrix


• • •

a11

b11

a12

•

• b12


• • •

a11

b11

a12

b12

a21

•

•b21


• • •

a11

b11

a22

•

a12

b12

• b22

a21

b21



b11

• a22

a12

b12

b22

a21

b21

•b31

a11

a31

•

•

a23

•a13

• a14

•b23

b13

b14 •

b11

a32

•

a22

a12b12

b22

a21

b21

b31

•

a11

• a31

•b32

a13

a14

b13

b14

b23

••b24

• a23

a24

•


a 62

b 22

b 21 a 63

a 64

•

a 54

b 14

a 61

b 31

a 53

b 23

a 52

b 32

a 44

b 24

a 51

b 41

a 43

b 33

a 42

b 42

a 34

b 34

a 41

b 51

a 33

b 43

a 32

b 52

a 24

b 44

a 31

b 61

a 23b 53

a 22

b 62

a 14

b 54

t 14

t 23

t 32

t 41

t 31

t 22

t 13

t 12

t 21

t 11

a 21 b 63b 64

•

Systolic Design —

Join Operation

character matching character matching systolic design — character matching a straightforward...

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