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

1. Longest Common Subsequence Algorithm on ASC Processors using Coterie Network Virdi Sabegh Singh (Advisor Dr. Robert A. Walker) Computer Science Department Kent State University

2. Presentation Outline • String matching and its variations • Motivation of LCS • Role of LCS in Molecular Biology • Genome matching • Overview of LCS • Overview of Folklore algorithm • Parallel Algorithms for LCS • Discussion on ASC processor

3. Presentation Outline • Brief introduction on Coterie Network • Longest Common Subsequence on Coterie Network • Exact match • Parallel SM algorithm and its Limitation • Longest Common Subsequence on Coterie Network • Approximate match • Summary and Future work

4. String Matching • String matching one of the most fundamental operation in computing. • May be two linear arrays of character can be compared to determine their similarity • One area where string matching gained interest is in the area of bioinformatics, in particular in the area of searching genetic databases • The string involved are how ever enormous, efficient string processing is therefore a requirement

5. String Matching Variations • Is Exact match the only solution? • What if the pattern does not occur in the text? • It still makes sense to find the longest subsequence that occurs both in the pattern and in the text. This is the longest common subsequence problem • Longest Common Subsequence, Longest Common Substring, Sequence alignment, Edit distance Problem are all variation of SM problem

6. Presentation Outline • String matching and its variations • Motivation ofLCS • Role of LCS in Molecular Biology • Genome Matching • Overview of LCS • Overview of Folklore algorithm • Parallel Algorithms for LCS • Discussion on ASC processor

7. Molecular Biology File comparison Screen redisplay Cheater finder Plagiarism detection Codes and Error Control Motivation of LCS • Spell checking • Human speech • Gas Chromatography • Bird song analysis • Data compression • Speech recognition

8. Presentation Outline • String matching and its variations • Motivation of LCS • Role of LCS in Molecular Biology • Genome matching • Overview of lcs • Overview of Folklore algorithm • Parallel Algorithms for LCS • Discussion on ASC processor

9. Role of lcs in Molecular biology • DNA sequences (genes) can be represented as sequences of 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

10. 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 e.g. 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

11. Presentation Outline • String matching and its variations • Motivation of LCS • Role of LCS in Molecular Biology • Genome Matching • Overview of lcs • Overview of Folklore algorithm • Parallel Algorithms for LCS • Discussion on ASC processor

12. Genome Matching • Genome: A Genome is a string of DNA bases A,C,G,T • In genetics application, the two string could correspond to two strands of DNA, which could, for example, come from two individuals, who we will consider genetically related, if they have a long subsequence common to their respective DNA sequences • The concept of subsequences of a string is different from the one of substring of a string • The string involved are how ever enormous, efficient string processing is therefore a requirement

13. Presentation Outline • String matching and its variations • Motivation of LCS • Role of LCS in Molecular Biology • Genome Matching • Overview of LCS • Overview of Folklore algorithm • Parallel Algorithms for LCS • Discussion on ASC processor

14. 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

15. Longest Common Subsequences • lcs can be reduced to other well known problem • 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

16. Presentation Outline • String matching and its variations • Motivation of LCS • Role of LCS in Molecular Biology • Genome Matching • Overview of lcs • Overview of Folklore algorithm • Parallel Algorithms for LCS • Discussion on ASC processor

17. Folklore Algorithm • Foundation of most of the LCS algorithm • 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);

18. Folklore Algorithm • Actually this time 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

19. Folklore Algorithm • 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, to calculate the best possible alignment, which leads us to the Smith-Water Man Algorithm • The Smith-Waterman Algorithm uses the same concept that of Folklore algorithm, but gives us the optimal result (LCS)

20. Folklore Algorithm A G A C T G A G G T A 00 0 0 0 0 0 0 0 0 0 0 A C T G A G 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 1 1 1 2 3 3 3 3 3 3 3 1 2 2 2 3 4 4 4 4 4 4 1 2 3 3 3 4 5 5 5 5 5 1 2 3 3 3 4 5 6 6 6 6

21. Presentation Outline • String matching and its variations • Motivation of LCS • Role of LCS in Molecular Biology • Genome Matching • Overview of lcs • Overview of Folklore algorithm • Parallel Algorithms for LCS • Discussion on ASC processor

22. Parallel Counterpart • Most of the 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

23. Computation Model • Various Network Models have been used to solve this lcs problem • Some algorithm uses 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

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

25. The ASC Processor • A scalable design implemented on a million gate Altera FPGA • SIMD-like architecture • Currently, 36 8-bit Processing Elements (PE) available • 8-bit Instruction Stream (IS) control unit with 8-bit Instruction and Data addresses, 32-bit instructions

26. Flynn’s Taxonomy

27. The ASC Architecture

28. 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

29. 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

30. 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 • This network has properties that are significantly different from the usual mesh • Because the processors in a group share common properties and purpose, we call the group a coterie, and hence the name coterie network

31. Presentation Outline • Brief introduction on Coterie Network • Longest Common Subsequence on Coterie Network • Exact match • Parallel SM algorithm and its Limitation • Longest Common Subsequence on Coterie Network • Approximate match • Summary and Future work

32. 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

33. 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

34. Coterie Network • There is still a single instruction stream, broadcasting of data values and collection of summary information are no longer restricted to a central entity, a capability that has previously been restricted to MIMD architecture • We refer this mode of parallelism as multiassociative, because the Coteries act as independent associative processors that share an instruction stream • Connection Machine-5 has such capabilities, but it was not purely SIMD system

35. 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)

36. 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 last two switches NE and NW are used to creation of eight way connected region Coteries Structure Coterie’s Physical Structure N NE NW V E W H WS ES S : Switch

37. 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

38. 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

39. Presentation Outline • Brief introduction on Coterie Network • Longest Common Subsequence on Coterie Network • Exact match • Parallel SM algorithm and its Limitation • Longest Common Subsequence on Coterie Network • Approximate match • Summary and Future work

40. Steps of LCS on Coterie Network • We assume, initially all the internal switch of the PEs are open • Let the Text string T=T(1)T(2)…T(n) been fed into row 1 of the coterie network • PE(0,j) stores T(j), where 0<=j<=n, as shown • This steps take unit time.

41. LCS Algorithm on Coterie Network A G A C T G A G G T A

42. PE’s form Coterie • PE’s with index value j as a constant forms m coteries as shown • Within each coteries operation Multicast is performed simultaneously, a constant time operation • The following slides shown the content of each PE after above operation

43. LCS Algorithm on Coterie Network A G A C T G A G G T A

44. LCS Algorithm on Coterie Network A G A C T G A G G T A A G A C T G A G G T A A G A C T G A G G T A A G A C T G A G G T A A G A C T G A G G T A A G A C T G A G G T A Content of each PE’s after MULTICAST operation

45. LCS Algorithm on Coterie Network • Let the Pattern string P=P(1)P(2)…P(m) been fed into column 1 of the coterie network • PE(i,0) stores P(j), where 0<=i<=m, as shown • This steps take unit time

46. LCS Algorithm on Coterie Network A C T G A G

47. PE’s form Coteries • PE’s with index value i as a constant forms n coteries as shown • Within each coteries operation Multicast is performed simultaneously, a constant time operation • The following slides show the content of each PE after above operation

48. LCS Algorithm on Coterie Network A C T G A G

49. LCS Algorithm on Coterie Network A C T G A G A C T G A G A C T G A G A C T G A G A C T G A G A C T G A G A C T G A G A C T G A G A C T G A G A C T G A G A C T G A G Content of each PE’s after MULTICAST operation

50. LCS Algorithm on Coterie Network • 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 Control register R. • This step takes unit time. • Next figure shows the value after this operation