Parallel Smith-Waterman Algorithm for DNA sequences Comparison on different cluster architectures

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1 Parallel Smth-Waterman Algorthm for DNA sequences Comparson on dfferent cluster archtectures Rucc Enzo, De Gust Armando E., Chchzola Franco. Insttuto de Investgacón en Informátca LIDI (III-LIDI) Facultad de Informátca Unversdad Naconal de La Plata. Argentna {erucc, degust, Abstract DNA sequence algnment s one of the most mportant operatons of bonformatcs. In 1981, Smth and Waterman developed a method for sequences local algnment. owever, n practce, varous heurstcs are used due to the processng and memory requrements of Smth and Waterman's algorthm. Even though they are faster, heurstcs do not ensure that the optmal algnment s found. For ths reason, t s nterestng to study how to apply the computer power of dfferent parallel platforms to speed up the sequence algnment process wthout losng result accuracy. In ths paper, a parallelzaton of Smth-Waterman algorthm s presented usng a ppelne scheme due to the data dependences nherent to the problem. Also, a comparatve analyss s carred out regardng the behavor of ths algorthm on dfferent multprocessor archtectures: heterogeneous cluster and multcore Fnally, the results obtaned wth the dfferent tests performed are presented, as well as future research lnes. Keywords: Bonformatcs, Sequence Algnment, Parallel Algorthms, Clusters, Multcores, eterogenety. 1 Introducton The study of dstrbuted and parallel systems s one of the most actve research lnes n Computer Scence nowadays [1][2]. In partcular, the use of multprocessor archtectures confgured n clusters, multclusters, grds and clouds, supported by networs wth varous characterstcs and topologes, has become general, not only for the development of parallel algorthms but also for the executon of processes that requre ntensve computaton and the provson of concurrent Web servces [3][4][5][6]. One of the areas of greatest nterest and growth n the last few years wthn the feld of parallel processng applcatons s that of the treatment of large volumes of data such as DNA sequences. The extensve comparson processng requred to analyze genetc patterns demands a sgnfcant effort n the development of effcent parallel algorthms [7]. Up to some years ago, the dea of a drect applcaton of computer methods n natural scences was odd and not very convncng. owever, t s now evdent that any serous advance n our nowledge and understandng of, for nstance, the complex mechansms of the cells, would be mpossble wthout the help of powerful algorthms and fast computers. DNA s the bologcal element that dfferentates speces, or the so-called types. Therefore, DNA sequence proflng s carred out as a worldwde effort. Wth the development of technques that allow unravelng the nformaton contaned n DNA, condtons were favorable for the emergence of bonformatcs, whch s a branch that sees not only to acqure, store and organze the bologcal nformaton contaned n DNA molecules, but also to analyze and nterpret these data. It nvolves the resoluton of complex problems usng tools provded by computatonal systems. The dagnoss and treatment of medcal condtons, the producton of genetcally enhanced foods, or the dentfcaton of lvng bengs focusng on traceablty or paternty systems are, among others, maor applcatons n the area. The more complete the genetc nformaton used for the analyss s, the hgher the certanty of the analyss wll be. The center for all bonformatc operatons and analyses s partly held by Sequence Algnment, both for pattern searchng among amno acd and nucleotde sequences, and for the search of phylogenetc relatonshps among organsms. The Smth-Waterman algorthm for local algnment s one of these methods; t focuses on smlar regons only n part of the sequences, whch means that the purpose of the algorthm s fndng small, locally smlar regons. Ths method has been used as the bass for many subsequent algorthms and s oftentmes used as basc pattern to compare dfferent algnment technques. If the length of the sequences nvolved are N and M, the complexty of the algorthm s O(NxM). Thus, the problem s escalated as the square of sequence sze [8]. Tang nto account that sequences can have up to 10 9 nucleotdes each, the tme and memory requred to solve ths problem n a sequental manner s mpractcable. Ths leads to the parallelzaton of the algorthm over powerful parallel archtectures.

2 1.1 Dstrbuted Parallel Archtectures The term cluster s appled to sets of computers bult wth standard hardware components that act as f they were an only computer [9]. Nowadays they play an mportant role for the soluton of problems from the scence, engneerng, and modern commerce felds [10]. Cluster technology has evolved to support actvtes that go from supercomputng applcatons and msson-crtcal software, web servers and e-commerce, to hgh-performance databases, among other uses. Clusters computng s the result of the convergence of several current trends, ncludng the avalablty of cheap hgh-performance processors and hgh-speed networs, the development of software tools for hgh-performance dstrbuted computaton, and the growng need for computer power for the applcatons that requre t [11]. Buldng cluster nodes s relatvely easy and economc due to ther flexblty: they can all have the same hardware confguraton and operatng system (homogeneous cluster), or they may have dfferent hardware and/or operatng system (heterogeneous cluster). Ths feature s an mportant factor when analyzng the performance that a cluster can offer as a parallel machne [12]. The technologcal change caused by energy consumpton and heat generaton problems that appear when escalatng processor speed has caused the appearance of multcores. Ths type of processors s formed by the ntegraton of two or more computer cores wthn the same chp, and ncreases applcaton performance by dvdng computng wor among all avalable cores [13] [14]. The ncorporaton of ths type of processors to conventonal clusters gves brth to an archtecture that combnes shared and dstrbuted memory, nown as multcore cluster [15][16]. 1.2 DNA Sequence Comparson on a Multcore Cluster and a eterogeneous Cluster In ths paper, the parallelzaton of Smth-Waterman algorthm s analyzed for the algnment of DNA to determne the smlarty degree between two large chans. The behavor of the parallel soluton on two dstrbuted archtectures s consdered: mult-core clusters and heterogeneous In ths context, t s mportant to study algorthm parallelzaton so that they are effcent n the dfferent clustertype dstrbuted archtectures: partally or totally dstrbuted memory [17][18]. In partcular, the approach of the applcaton to study s attractve due to ts complexty and the possblty of breang down parallel algorthm concurrency nto blocs of dfferent dmensons, whch allows an optmal adaptaton of the applcaton to the support archtecture. In Secton 2, the Smth-Waterman algorthm s explaned, together wth the sequental and the parallel solutons used n ths paper. In Secton 3, the expermental wor carred out s descrbed, whereas n Secton 4, the results obtaned are presented and analyzed. Secton 5 presents the conclusons and future lnes of wor n relaton to ths paper. 2 Smth-Waterman Algorthm Defnton Ths method allows algnng two DNA sequences by nsertng gaps (f necessary) that are used to detect locally smlar regons that may ndcate the presence of a relaton between both sequences, whch s done by assgnng a smlarty score. If gaps are nserted, that s, certan elements of the sequences are not algned to acheve a better overall algnment, a penalzaton s appled. The algorthm calculates a smlarty score between two sequences and then, f necessary, employs a bacwards algnment process for an optmal result [7]. The followng paragraphs explan the operaton of the algorthm to fnd a smlarty score between two DNA sequences. Gven two sequences: A = a 1 a 2 a 3 a M and B = b 1 b 2 b 3 b N, a matrx of (N+1)x(M+1) s bult, n such a way that the nucleotde bases that form sequence A label the rows (startng wth 1), and those from sequence B label the columns (startng wth 1). The followng steps are appled to calculate the values of that wll yeld the smlarty score between A and B: a. Start row 0 and column 0 of wth 0, as ndcated n Equaton for 0 N and 0 M (1) 0 b. Calculate the value of, [1,..,N] and [1,..,M] by means of Equaton 2. Ths value ndcates the maxmum smlarty between two segments endng n a and b, respectvely. 0 max C F 1, 1 V ( a, b ) (2) V(a, b ) s the matchng functon that ndcates the score obtaned for matchng a wth b. It s based on a table of values called substtuton matrx that descrbes the probablty of a nucleotde base from sequence A at poston to occur n sequence B at poston. The most common matrx s the one that rewards wth postve value when a and b are dentcal, and punshes wth a negatve value otherwse.

3 C s the score n column consderng a gap, and s calculated wth Equaton 3. C max 1 {, g( )} (3) F s the score n row consderng a gap, and s calculated wth Equaton 4. F max 1 l {, g( l)} (4) l g(x) s the penalzaton functon for a gap of length x, and s obtaned wth Equaton 5, q beng the penalzaton appled for openng a gap and r the penalzaton for prolongng t. g ( x) q rx ( q 0; r 0) (5) c. The smlarty score s obtaned as shown n Equaton 6. G max { ) } (6) ( 0 N)(0 M d. Based on the poston n matrx where the value G was found (representng the end of the hghest-scorng algnment between both sequences), a bacwards process s performed to obtan the par of segments wth maxmum smlarty, untl a poston whose value s 0 s reached, ths beng the startng pont of the segment. 2.1 Sequental Soluton of Smth-Waterman Algorthm In ths secton, the sequental soluton of Smth- Waterman algorthm s analyzed wth the purpose of determnng the smlarty score between two DNA sequences. Ths means that the bacwards process s not taen nto account when obtanng the segment that represents the optmal algnment (step d of the algorthm explaned n the prevous secton s not performed). Sequence B Sequence A F (gap) d C (gap) Fg. 1. Data dependency scheme. Fgure 1 shows the data dependency that exsts for calculatng matrx values. To obtan,, the result of -1,-1 ( d n Fgure 1) s requred, and the score must be nown when consderng a gap n row and another one n column. Ths restrcton allows calculatng values from top to bottom and left to rght ( 11, 12, 13, 21, 22, 23,..). Tang nto account that step d of the algorthm s not carred out, matrx does not have to be stored n full, all that s needed s: A vector h of length M+1 that at each poston eeps the value obtaned n the last processed row over that column. Equaton 7 shows the values for h correspondng to the example shown n Fgure 1., 1 h (7) 1, 1 An element e to temporarly store the last value calculated n the row that s beng processed. In Fgure 1, e =,-1. A vector c of length M+1 that at each poston eeps the maxmum score consderng a gap n that column. Equaton 8 shows the values for c correspondng to the example shown n Fgure 1. c C C 1, (8) An element f that eeps the maxmum score consderng a gap n the row that s beng processed. In the example shown n Fgure 1, f = F, General Parallel Soluton of Smth- Waterman Algorthm The data dependency mentoned n the prevous secton causes the problem to be solved followng a ppelne scheme where S stages perform the same wor over varous consecutve nucleotde subsets of the frst sequence (A n Fgure 1). In each cycle, stage s (for [1, S-1]) receves a data bloc from s -1, solves part of ts wor, and then sends these results to s +1 (except for the last stage whch does not need to send ts results to any other stage). The frst stage (s 0 ) only performs ts wor by sendng partal results (correspondng to a bloc) to ts successor. An mportant aspect of ths soluton s selectng the number of elements (BS) from sequence B that form the data blocs that are sent from one process to another, tang nto account that: Ppelne parallelsm s exploted to ts maxmum capacty only after S-1 cycles have been processed. That s, when all stages have receved wor to do. The larger the BS, the longer the tme requred to fll the ppe, and therefore, the lower ts explotaton. From ths pont of vew, BS should tend to 1. If the sze of BS s very small, the stages spend more tme communcatng partal results than actually processng nformaton. From ths pont of vew, BS should tend to N. A sutable bloc sze should be found, so that data communcaton and data processng can be done smultaneously. The optmal sze does not only depend on the

4 archtecture used, but also on the communcaton model mplemented. In prevous wors, a procedure for calculatng the optmal value of BS based on archtecture characterstcs and sequence sze has been establshed [19] Message Passng as Communcaton Model In ths case, each ppelne stage s carred out by a dfferent process p (for [0, S-1]), and partal results are communcated by sendng messages between consecutve processes. The frst sequence (A n Fgure 1) s dstrbuted by p 0 among the S processes that form the ppelne DNA Sequence Dstrbuton For the parallel soluton to be effcent, wor load should be balanced, that s, all processes should wor for the same tme. If the archtecture beng used s homogeneous, all that s needed s dstrbutng the frst sequence (A n Fgure 1) equally among the varous processes that form the parallel applcaton to acheve a balanced soluton. If an heterogeneous archtecture s beng used, balancng the wor load s more complex because t depends on the power of each processng unt (PU). To do ths, two concepts that characterze the archtecture beng used are appled: the relatve computer power (rcp) and the total computer power (tcp). Each processng unt s characterzed by ts relatve computer power (rcp ) wth respect to the most powerful PU, and s calculated as shown n Equaton 9. rcp Power (PU ) (9) Power (PU ) On the other hand, total computer power (tcp) reflects the power of the archtecture as a whole wth respect to the most powerful processng unt, and s calculated as shown n Equaton 10 (assumng an archtecture wth P processng unts). best the processng unt where p s located (rcp). Ths s shown n Equaton 11. m M rcp (11) tcp Process p 0 sends the entre second sequence (B n Fgure 1) to processes p, for = 1..S-1. 3 Expermental Wor The language used for mplementatons s C wth the MPI lbrary (OpenMPI) to manage communcatons between processes. 3.1 Archtectures Used To analyze the behavor of the algorthm, tests were carred out on two dfferent archtectures: A standard cluster wth three types of monoprocessor machnes (26 n total) communcated through a 100 Mbts Ethernet networ. The characterstcs of each computer type are: - Type 1: Pentum IV 2.4 Ghz, 1 Gb RAM memory. - Type 2: Celeron 2 Ghz, 128 Mb RAM memory. - Type 3: Pentum III 700 Mhz, 256 Mb RAM memory. A mult-core cluster: Blade wth 8 blades, each wth 2 quad core Intel Xeon e Gz processors. Each blade has 2 Gb RAM memory (shared between both processors) and 2 x 6Mb L2 cache for each par of cores [20][21]. 3.2 Tests carred out wth the standard cluster To carry out these tests, frst the relatve computer power of each type of processor must be determned for ths type partcular of applcaton. Ths value s obtaned by runnng the sequental algorthm (wth relatvely small sequences, N=M < 2500) on each type of computer. Table 1 shows the computer power of each type of computer relatve to the most powerful PU (type 1). P 1 0 tcp rcp (10) Based on these characterstcs, a generc soluton can be obtaned both for homogeneous and heterogeneous archtectures. The dstrbuton of sequences (A and B n Fgure 1) s done as follows: Process p 0 dstrbutes the elements of the frst sequence (A n Fgure 1), assgnng m consecutve nucleotdes to p, for = 0..S-1. Where m s determned based on the relatve computer power of Table 1. Relatve computer power of each type of processor. Tests were carred out on subsets of the 26 computers mentoned n Secton 3.1 to obtan the dfferent total computer powers: 3.2, 5.8, 12.2, 17, 21. Usng 4, 8, 16, 24 and 26 processors, respectvely.

5 DNA sequences of varous lengths (20000; 40000; 80000; ; ) were also taen. Table 2 shows the optmal bloc sze (BS) used n each test n accordance wth the functon descrbed n prevous wors [19]. whch wor s beng carred out (whch determnes the theoretcal speedup), as ndcated n Equaton (13). Speedup Effcency (13) tcp Table 4 shows the effcency acheved by the algorthm on the heterogeneous cluster for the dfferent sequence szes and processor subsets. Fgure 2 s a chart representaton of those same values. Table 2. Bloc sze BS used n each test run on the heterogeneous 3.3 Tests carred out wth the multcore cluster Tests were carred out usng dfferent numbers of processng unts (cores): 4, 8, 16, 32 and 64. Sequence szes were the same as those used for the tests mentoned n 3.2 [22]. All cluster cores beng equal, the total computer power of the archtecture s gven by the number of cores used, snce rcp = 1 for all processng unts. Table 3 shows the optmal bloc sze (BS) used n each test n accordance wth the functon descrbed n prevous wors [19]. From the results shown n the chart, t can be seen that the algorthm obtans a good effcency, especally consderng the nteracton model used (ppelne). Ths effcency remans wthn the range [ ], except when usng small sequence szes n large archtectures. Ths s because the rato between the tme durng whch the ppelne s not worng n all ts stages and the tme the ppelne s full s greater, snce there are many stages and less data to be processed. As t s to be expected, when problem sze ncreases, effcency also ncreases, whereas when the total computer power of the archtecture (tcp) ncreases due to a larger number of processors beng used, effcency decreases. Table 4. Effcency acheved durng the tests run on the heterogeneous Table 3. Bloc sze BS used n each test run on the multcore 4 Results To assess the behavor of the algorthms developed when escalatng the problem and/or the archtecture, the speedup and effcency of the tests carred out are analyzed [1][3][11][23]. The speedup metrcs s used to analyze the algorthm performance n the parallel archtecture as ndcated n Equaton (12). Sequental Tme Speedup (12) ParallelTme In heterogeneous archtectures, the Sequental Tme s gven by the tme of the best sequental algorthm executed n the machne wth the greatest calculaton power. Parallel Tme s the end tme for the entre system. To assess how good the speedup obtaned s, effcency s calculated. To ths am, the speedup obtaned s compared wth the total computng power (tcp) of the archtecture upon Fg. 2. Effcency acheved durng the tests run on the heterogeneous Table 5 shows the effcency acheved by the algorthm on the multcore cluster for the dfferent sequence szes and core subsets. Fgure 3 s a chart representaton of those same values. Ths chart shows that the multcore cluster offers a greater ncrease n effcency when sequence sze ncreases, and smlarly, there s a greater decrease n effcency when the number of cores n the archtecture ncreases.

6 If we compare the behavor of the algorthm n both archtectures, the multcore cluster offers a better performance than the heterogeneous Ths s partly due to the fact that communcaton speed s hgher n the mult-core cluster, whch allows worng wth smaller bloc szes BS. By reducng bloc sze BS, the ppelne s full durng more cycles, whch results n a better explotaton of the parallelsm. Analyss of the mpact of heterogenety when escalatng the problem. 6 References [1] Grama A., Gupta A., Karyps G., Kumar V., "An Introducton to Parallel Computng. Desgn and Analyss of Algorthms. 2nd Edton". Pearson Addson Wesley [2] Ben-Ar, M. "Prncples of Concurrent and Dstrbuted Programmng, 2/E". Addson-Wesley, Table 5. Effcency acheved durng the tests run on the multcore [3] Dongarra J., Foster I., Fox G., Gropp W., Kennedy K., Torczon L., Whte A., "The Sourceboo of Parallel Computng". Morgan Kauffman Publshers. Elsever Scence [4] Juhasz Z. (Edtor), Kacsu P. (Edtor), Kranzlmuller D. (Edtor), "Dstrbuted and Parallel Systems: Cluster and Grd Computng". Sprnger; Frst Edton [5] D Stefano M., "Dstrbuted data management for Grd Computng". John Wley & Sons Inc [6] Mller M., "Cloud Computng: Web-Based applcatons that change the way you wor and collaborate onlne". QUE Publshng Fg. 3. Effcency acheved durng the tests run on the multcore 5 Conclusons In ths paper, Smth-Waterman algorthm s parallelzed for the algnment of DNA sequences by means of a ppelne scheme due to the dependency of data that s nherent to the problem. A multcore cluster (8 blades wth 8 cores each) and a heterogeneous cluster of monoprocessor computers (26 n total, 3 dfferent types) are used as expermental archtectures. The behavor of ths algorthm runnng on these archtectures was analyzed, and t was observed that both cluster types yeld hgh effcency levels. The multcore cluster s slghtly superor because ts faster communcaton speed between processes reduces the overhead. On the other hand, the lac of load balance caused by the lac of accuracy when calculatng the relatve computer power of each type of processor of the heterogeneous cluster causes the yeld obtaned wth ths type of archtecture to slghtly drop. Future lnes of wor focus on three aspects: Soluton scalablty studes (n relaton to sequence sze and number of processors n the cluster). [7] Attwood T. K., Parry-Smth D. J., "Introduccón a la Bonformátca". Pearson Educaton S.A [8] Zhang F., Qao X., Lu Z., "A Parallel Smth-Waterman Algorthm Based on Dvde and Conquer". Proceedng of the Ffth Internatonal Conference on Algorthms and Archtecture for Parallel Processng [9] Grd Computng and Dstrbuted Systems (GRIDS) Laboratory - Department of Computer Scence and Software Engneerng (Unversty of Melbourne), "Cluster and Grd Computng" [10] Zoltan J., Kacsu P., Kranzlmuller D., Dstrbuted and Parallel Systems: Cluster and Grd Computng. The Internatonal Seres n Engneerng and Computer Scence. Sprnger; 1st edton, [11] Wlnson B, Allen M, Parallel Programmng. Technques and Applcatons Usng Networed Worstatons and Parallel Computers, 2da Edcón, Pearson Prentce all, [12] Al-Jarood J, Mohamed N, Jang, Swanson D. Modelng parallel applcatons performance on heterogeneous system. IEEE Computer Socety, 2003.

7 [13] AMD, "Evolucón de la tecnología de múltple núcleo" amd.com/es-es/amd-mult- Core/resources/Technology-Evoluton. [14] Burger T. W., "Intel Mult-Core Processors: Quc Reference Gude". /cachewww.ntel.com/cd/00/00/23/19/231912_ pdf [15] Mc Cool M., "Programmng models for scalable multcore programmng" [16] Cha L., Gao Q., Panda D. K., "Understandng the mpact of mult-core archtecture n cluster computng: A case study wth Intel Dual-Core System". IEEE Internatonal Symposum on Cluster Computng and the Grd 2007 (CCGRID 2007), pp [17] De Gust L., Chchzola F., Naouf M., De Gust A., Luque E., "Automatc Mappng Tass to Cores - Evaluatng AMTA Algorthm n Multcore Archtectures". IJCSI Internatonal Journal of Computer Scence Issues, Vol. 7, Issue 2, No [18] Bertogna M., Grosclaude E., Naouf M., De Gust A., Luque E., "Dynamc on Demand Vrtual Clusters n Grds". 3rd Worshop on Vrtualzaton n gh-performance Cluster and Grd Computng (VPC 08). Span [19] Chchzola Franco, "Estudo analítco de TB óptmo en base a caracterstcas del cluster". Techncal report III-LIDI [20] P, "P BladeSystem". [21] P, "P BladeSystem c-class archtecture". c /c pdf. [22] Rucc E., "Comparacón de modelos de sncronzacón en programacón paralela sobre cluster de multcores ", Tesna de grado, Unversdad Naconal de La Plata, [23] Leopold C., "Parallel and Dstrbuted Computng. A survey of Models, Paradgms, and Approaches". Wley, New Yor

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