Virdi Sabegh Singh (Advisor Dr. Robert A. Walker) Computer Science Department

Virdi Sabegh Singh(Advisor Dr. Robert A. Walker)Computer Science Department

Kent State University

Solving the Longest Common Subsequence (LCS) problem using the Associative ASC Processors with Reconfigurable 2D Mesh

Presentation Outline String matching and its variations Motivation of LCS Role of LCS in Molecular Biology Overview of LCS Discussion on Folklore algorithm Parallel Algorithms for LCS Discussion on ASC processor Brief introduction on Coterie Network

Presentation Outline Reconfigurable Network in the ASC

Processor Modifying the Network for LCS Algorithm Longest Common Subsequence on

Reconfigurable 2D Mesh Exact match

Longest Common Subsequence on Reconfigurable 2D Mesh Approximate match

Summary and Future work

Presentation Outline String Matching and its variations Motivation of LCS Role of LCS in Molecular Biology Overview of LCS Discussion on Folklore algorithm Parallel Algorithms for LCS Discussion on ASC processor Brief introduction on Coterie Network

String Matching Fundamental operation in computing Comparison of characters, words etc. to

determine their similarity Interest is in the area of bioinformatics, in

particular searching genetic databases String are enormous, efficient string

processing is therefore a requirement

String MatchingVariations Is Exact match the only solution? What if the pattern does not occur in the

text? Find the longest subsequence that occurs

both in the pattern and in the text. Longest Common Subsequence, Longest

Common Substring, Sequence alignment, Edit distance Problem are all variation of SM problem

Sequence alignment Procedure of comparing 2 or more sequences Searches series of individual character pattern in the

same order in the sequence

LCS Find a common string for both the sequences preserving

symbol order

Sequence alignment vs. LCS

GGHSRLILSQLGEEG.RLLAIDRDPQAIAVAKT....IDDPRFSII

GGHAERFL.E.GLPGLRLIGLDRDPTALDVARSRLVRFAD.RLTLV|||::::| : |::| ||:::||||:|:|||:: ::| |::::


Motivation of LCS

Molecular Biology File comparison Screen redisplay Cheater finder Plagiarism

detection Codes and Error

Control

Spell checking Human speech Gas Chromatography Bird song analysis Data compression Speech recognition


Role of LCS in Molecular biology DNA sequences (genes) represented by

four letters ACGT, corresponding to the four submolecules forming DNA

When biologists find a new sequences, they typically want to know what other sequences it is most similar to

One way of computing how similar (homologous) two sequences are is to find the length of their longest common subsequence

Role of LCS in Molecular biology This is a simplification, since in the biological

situation one would typically take into account not only the length of the LCS, but also i.e., how gaps occur when the LCS is embedded in the two original sequences.

An obvious measure for the closeness of two strings is to find the maximum number of identical symbols (preserving symbol order)

This by definition, is the longest common subsequence of the strings


Longest Common Subsequences

Formally, we compare two strings, X[1..m] and Y[1..n], which are elements of the set Σ*; here Σ denotes the input alphabet containing σ symbols

The LCS of strings X and Y, lcs(X,Y) is a common subsequences of maximal length

Special case of the edit distance problem The distance between X and Y is defined as the minimal

number of elementary operations needed to transform the source string X to the target string Y

In practical applications, operation are restricted to insertions, deletions and substitutions

For each operation, an application dependent cost is assigned

Longest Common Subsequences LCS(X,Y) typically solved with the dynamic

programming technique and filling an mxn table

Table elements acts as a vertices in a graph, and the simple dependencies between the table values defines the edges

The task is to find the longest path between the vertices in the upper left and lower right corner of the table


Folklore Algorithm Foundation of most of the LCS algorithms Given two strings, find the LCS common to both

strings. Example:

String 1: AGACTGAGGTA String 2: ACTGAG

AGACTGAGGTA - -ACTGAG - - - list of possible alignments - -ACTGA - G- - A- -CTGA - G- - A- -CTGAG - - -

The time complexity of this algorithm is clearly O(nm);

Folklore Algorithm Complexity does not depend on the sequences u

and v themselves but only on their lengths By choosing carefully the order of computing the

d(i,j)'s one can execute the above algorithm in space O(n+m)

The bottleneck in efficient parallelization of LCS problem are the calculating the value of diagonal elements, as shown

As seen, the value of {i,j} depend upon the previous element {i-1,j-1}, when a match is found.

We may have more then one LCS for the same problem

In order to find the best LCS, we associate some parameter

The Smith-Waterman Algorithm uses the same concept that of Folklore algorithm, but gives us the optimal result (LCS)

Folklore Algorithm

Folklore Algorithm

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A G A C T G A G G T A

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Parallel Counterpart Serial LCS algorithm runs in O(nm) time, where n is the

length of the text string, and m is the length of pattern string

Efficient Parallel algorithm do exist to solve this computational extensive task Some algorithm runs in O(max{n,m}) using O(min{n,m}) processors O(logn) using O(mn/logn) processors There are constant time algorithm for this LCS

problem using the DP approach, using some assumptions

Computation Model Various Network Models have been used to solve

this LCS problem PRAM model, Suffix Tree, 2D-Mesh Network,

Mesh with Reconfigurable buses, Mesh with Multiple buses etc

Algorithm which runs in constant time, assume that most of the operation are done in constant time

In parallel version, one of the important task is to distribute data efficiently and easy manner


The ASC Processor A scalable design implemented on a

million gate Altera FPGA SIMD-like architecture Searches data by content instead of

address 8-bit Instruction Stream (IS) control unit

with 8-bit Instruction and Data addresses, 32-bit instructions

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PE and Memory

Netw

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PE and Memory

PE and Memory

PE and Memory

CommonRegisters

ResponderResolution

Unit

PE Array

ControlUnit

Instr

ucti

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Bu

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Data

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From Control Unit

The ASC Architecture

The ASC Architecture Each PE listens to the IS through the

broadcast and reduction network PEs can communicate amongst

themselves using the PE Network PE may either execute or ignore the

microcode instruction broadcast by IS under the control of the Mask Stack

The ASC Features Associative Search

Each PE can search its local memory for a key under the control of IS

Responder Resolution A special circuit signals if ‘at least one’ record

was found Masked Operation

Local Mask Stacks can turn on or off the execution of instruction from IS

Communication between PE’s In 2D mesh network,

Communication between P.E’s themselves take place in two different ways

By using the nearest neighbors mesh interconnection network

Powerful variation on the nearest-neighbor mesh called the “Coterie network”, developed in response to the requirement for nonlocal communication

Processors in a group share common properties and purpose, we call the group a coterie, and hence the name coterie network


Coteries[ Weems & Herbordt ]“A small often selected group of persons who

associate with one another frequently” Features:

Related to other Reconfigurable broadcast network Describable using hypergraphs And they are dynamic in nature

Advantages: Propagation of information quickly over long

distances at electrical speed Support of one-to-many communication within

coterie, reconfigurability of the coterie

Coterie Network Provides method of performing operations on

regions of an image in parallel Used extensively for Matrix Arithmetic, FFT,

Convex Hull Computation, Simulating a pyramid processors, General Permutation Routing and Parallel Prefix

Note that the coterie network is separate from the nearest-neighbor mesh, which we refer to as the SEWN network

Coterie network results in a new mode of parallelism that falls between SIMD and MIMD

PE’s form Coteries

5 x 5 coterie network with switches shown in “arbitrary” settings. Shaded areas denotes coterie (the set of PEs Sharing same circuit)

Coterie’s Physical Structure In the physical

implementation, each PE controls set of switches Four of these switches

control access in the different directions (N,S,E,W)

Two switches H and V are used to emulated horizontal and vertical buses

The two switches NE and NW are used to creation of eight way connected region

Coteries Structure

NWNE

WSES

V

H E

S

W

: Switch

N

Coterie Network The isolated group of processors called

coterie’s, have access only to the multicast within a coterie

When the switches are set, connected processors form a Coterie

The coterie network switches are set by loading the corresponding bits of the mesh control register in each P.E

Basic Coterie structure algorithm The complexity is assumed to be O(1)

unless otherwise stated Transfer of data between two adjacent coteries Symmetry breaking between a pair of nodes in

a coterie Two nodes within a coterie exchange

information






Reconfigurable Network in the ASC Processor Scalable design with

Reconfigurable network Can be used as dedicated

ASIC or Co-processor Implemented on Altera

APEX20KC1000, single CPU, 50 pipelined PE & linear PE interconnection network

Key to reconfigurability is the Data Switchinside each PE S

N

W E

DATA SWITCH

Reconfigurable Network in the ASC Processor Linear network, PE communicates both

ways 2D Reconfigurable Network, PE

communicates with all of its neighbors (N-E-S-W)

Data switch has bypass mode to allow PE communication to skip non-responder, so as to support Associative computing


Processor Modifying the Network for LCS

Algorithm Longest Common Subsequence on




Modifying the Network for LCS Algorithm Coterie Network, one of the powerful network But we don’t need full features of the same for

the LCS Algorithm Augmented ASC with new 2D Mesh, with row and

column broadcast buses Modified linear network into 2D Mesh Added features inspired by Coterie network A PE can communicate now, with any of its four

neighbors Bypass mode augmented to support H and V

bypass as well






LCS Algorithm on Reconfigurable 2D Mesh We assume, initially all the internal switch

of the PEs are open Each PEs have a Match Register “M” and

Length Register “L”, initially having value 0 Let the Text string T=T(1)T(2)…T(n) been

fed into row 1 of the Reconfigurable 2D Mesh

PE(0,j) stores T(j), where 0<=j<=n, as shown

This steps take unit time.

LCS Algorithm on Reconfigurable 2D Mesh

A G A C T G A C T G A

LCS Algorithm on Reconfigurable 2D Mesh Broadcast each character of the text string

along the column, using column broadcast bus

In case of Coterie network Form coteries along the column Perform operation multicast in all coteries This step takes unit time.









Let the Pattern string P=P(1)P(2)…P(m) been fed into column 1 of the Reconfigurable 2D Mesh

PE(i,0) stores P(j), where 0<=i<=m, as shown

This steps take unit time


A

C

T

G

A

C

PE’s form Coteries Broadcast each character of the Pattern

string along the row, using row broadcast bus

In case of Coterie network Form coteries along the rows Perform operation multicast in all coteries This step takes unit time


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LCS Algorithm on Reconfigurable 2D Mesh After this step each PE’s with index [i,j]

have P[i] T[j]. Now each PE’s compares the content held

in his internal Register. It set the value 1 if they are equal else 0 in

its Match register M. This step takes unit time. Next figure shows the value after this

operation


1 0 1 0 0

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100010

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00010001

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Parallel VLDC SM Algorithm on MCCRB Network A Parallel SM algorithm With VLDC

proposed by K.L. Chung in 1995 Uses the Mesh-Connected Computer with

reconfigurable buses system. Runs in O(1) time Pattern of size m , Text of size n uses,

O(nm) PE’s.

LCS Algorithm on Reconfigurable 2D Mesh Now expect the PE’s with index[0,j], where

0<=j<=n, all PEs having value 0 in its Match register M closes the N-E switch.

PE’s with value 1 in its Match Register M closes the W-S switch as shown

Both the steps takes unit time


1 0 1 0 0

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LCS Algorithm on Reconfigurable 2D Mesh Sequential Version:

Each PE at the beginning (bottom) of an LCS sends a token to its West neighbor

A PE receiving a token adds 1 to its token if its Match Register “M” Contains 1, and passes the token on if its W-S bypass switch is set and stores it in its Length Register “L”

Perform operation MAX on the entire network The PE with the largest value in its Length

register “L” is the start of the LCS Complexity being the length of the LCS found


1 0 6 0 0

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LCS Algorithm on Reconfigurable 2D Mesh Parallel Version:

Each PE a the beginning (bottom) sends its [row, column] id to its west neighbor

PE receiving an ID passes it on Or is it’s the end of an LCS subtracts its own ID

from the received ID Store the value in the Length Register “L” Perform operation Max on the network PE having largest value in its Length Register

“L” is the start of the LCS Complexity, Constant time


1,1 1,2 1,3 1,4 1,5

02,1

0003,1

0 02,80002,4

1,111,101,91,81,71,6

3,5

4,1

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0004,60004,2

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LCS Algorithm on Reconfigurable 2D Mesh Exact match implemented on Altera

APEX1000KC FPGA Sufficient to hold 6 x 11 arrays of PEs,

used in the example Ran at a clock speed of 37 MHz, with

respect to the number of PEs Larger network can be easily supported,

due to ASC scalability

LCS Algorithm on Reconfigurable 2D Mesh The algorithm described above solve the

LCS problem for exact match Doesn’t address approximate match The next example demonstrate this

problem For the string:

Text : AGACTGAGGTA Pattern : ACCAGG LCS being : ACAGG







1 0 1 0 0

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LCS Algorithm on Reconfigurable 2D Mesh Inject token from the bottom row Token reaches a gap, enter south port of

some PE, and stops at that PE, whose W-S switch is not set

Close the W-S bypass switch of that PE, and bypass Vertically (N-S) of all to the top of the PEs identified in above step

LCS Algorithm on Reconfigurable 2D Mesh Inject token from the top row Token reaches a gap, enter West port of

some PE, and stop at that PE whose W-S switch is not set

Close the W-S bypass switch of that PE, and Bypass Horizontally (W-S) of all PEs to the right of the PE identified in above step

Bypass W-S switch of all those PEs, where there is cross over of H and V switch

LCS Algorithm on Reconfigurable 2D Mesh Inject token from the bottom row PE receiving a token adds 1 to its Match

Register “M” contains 1 and passes it on if its W-S bypass switch is set, if ends of LCS stores it in the Length Register “L”

The PE with the largest value in its “L” register is the start of LCS

Increment “L” by 1, if “M” register has value 1

LCS Algorithm on Reconfigurable 2D Mesh When H or V switch are set, the token

bypass this switch, the “L” value remains unchanged

We bypass only those tokens whose, value in the “M” Match register is maximum and that in “L” Length register is Minimum.

If both the token have “M” value same, block that token having “L” value maximum

If both “L” and “M” value are same, select any one of them


1 0 1 0 0

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Summary and Future work Summary:

In this Presentation, we have described a new parallel algorithm on specialized hardware

Inspired by certain feature of Coterie Network Modified ASC processor to add reconfigurable

2D Mesh Exact Match implemented on Altera FPGA Constant time algorithm for Exact match Approximate algorithm depends upon the

diameter of the network

Summary and Future work Future Work:

Optimize the algorithm for Approximate match

Incorporating additional parameters to find the best LCS, instead of longest one

Incorporating different weights schemes Conserve memory by using encoding

scheme Use two bits to represent four bases of DNA Using this idea, we save 75% of space/memory

Acknowledgements Professor Walker Committee members for their time ASC/MASC Group for their useful

Comments Professor Helen Piontkivska from Biology

Department Professor Charles Weems and Martin

Herbordt Hong Wang for implementing the exact

match algorithm on FPGA

THANK YOU

Questions….

Virdi Sabegh Singh (Advisor Dr. Robert A. Walker) Computer Science Department

Documents

longest subsequence

coterie networkrole

common string

common substring

asc processormodifying

molecular biologythis

new sequences

original sequences