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 |||::::| : |::| ||:::||||:|:|||:: ::| |::::

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

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

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

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

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

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

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

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

A G A C T G A G G T A ACTGAGACTGAG

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

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

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

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

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

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

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 NW NE WS ES 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

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

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 Switch inside each PE S N WE 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

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

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

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

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.

LCS Algorithm on Reconfigurable 2D Mesh A G A C T G A C T G A

LCS Algorithm on Reconfigurable 2D Mesh  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

LCS Algorithm on Reconfigurable 2D Mesh 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

LCS Algorithm on Reconfigurable 2D Mesh ACTGACACTGAC ACTGACACTGAC ACTGACACTGAC ACTGACACTGAC ACTGACACTGAC ACTGACACTGAC ACTGACACTGAC ACTGACACTGAC ACTGACACTGAC ACTGACACTGAC ACTGACACTGAC

 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

LCS Algorithm on Reconfigurable 2D Mesh A G A C T G A C T G A ACTGACACTGAC

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

LCS Algorithm on Reconfigurable 2D Mesh A G A C T G A C T G A ACTGACACTGAC

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

LCS Algorithm on Reconfigurable 2D Mesh A G A C T G A C T G A ACTGACACTGAC

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

LCS Algorithm on Reconfigurable 2D Mesh 1,11,21,31,41,5 0 2, ,1 00 2, ,4 1,111,101,91,81,71,6 3,5 4,1 6,1 5, , ,2 3, , ,7 00 6,4 00 6,8 0 4, , A G A C T G A C T G A ACTGACACTGAC

LCS Algorithm on Reconfigurable 2D Mesh A G A C T G A C T G A ACTGACACTGAC

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

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

LCS Algorithm on Reconfigurable 2D Mesh A G A C T G A G G T A ACCAGGACCAGG

LCS Algorithm on Reconfigurable 2D Mesh A G A C T G A G G T A GACAGGGACAGG

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

LCS Algorithm on Reconfigurable 2D Mesh A G A C T G A G G T A ACCAGGACCAGG

LCS Algorithm on Reconfigurable 2D Mesh A G A C T G A G G T A GACAGGGACAGG

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

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

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