PARALLEL ALGORITHMS FOR MAPPING SHORT DEGENERATE AND WEIGHTED DNA SEQUENCES TO A REFERENCE GENOME

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1 International Journal of Foundations of Comuter Science c World Scientific Publishing Comany PARALLEL ALGORITHMS FOR MAPPING SHORT DEGENERATE AND WEIGHTED DNA SEQUENCES TO A REFERENCE GENOME COSTAS S. ILIOPOULOS Det. of Comuter Science, King s College London, London WC2R 2LS, UK & Digital Ecosystems & Business Intelligence Institute, Curtin University, GPO Box U1987 Perth WA 6845, Australia csi@dcs.kcl.ac.uk MIRKA MILLER School of Electrical Engineering and Comuter Science, The University of Newcastle, Callaghan NSW 2308, Australia & Det. of Mathematics, University of West Bohemia, Pilsen, Czech Reublic& Det. of Comuter Science, King s College London, London WC2R 2LS, UK mirka.miller@newcastle.edu.au SOLON P. PISSIS Det. of Comuter Science, King s College London, London WC2R 2LS, UK solon.issis@kcl.ac.uk Received (Day Month Year) Acceted (Day Month Year) Communicated by (xxxxxxxxxx) One of the most ambitious trends in current biomedical research is the large-scale genomic sequencing of atients. Novel high-throughut (or next-generation) sequencing technologies have redefined the way genome sequencing is erformed. They are able to roduce millions of short sequences (reads) in a single exeriment, and with a much lower cost than reviously ossible. Due to this massive amount of data, efficient algorithms for maing these sequences to a reference genome are in great demand, and recently, there has been amle work for ublishing such algorithms. One imortant feature of these algorithms is the suort of multithreaded arallel comuting in order to seedu the maing rocess. In this aer, we design arallel algorithms, which make use of the message-assing arallelism model, to address this roblem efficiently. The roosed algorithms also take into consideration the robability scores assigned to each base for occurring in a secific osition of a sequence. In articular, we resent arallel algorithms for maing short degenerate and weighted DNA sequences to a reference genome. Keywords: arallel algorithms; string algorithms; next-generation sequencing Mathematics Subject Classification: 22E46, 53C35, 57S20 1

2 2 COSTAS S. ILIOPOULOS, MIRKA MILLER, SOLON P. PISSIS 1. Introduction The traditional Sanger caillary sequencing methods [22, 23], develoed in the mid 70 s, have been the workhorse technology for DNA sequencing, for almost 30 years, and is still the go-to technique for high-quality sequencing. But sequencing technology has come a long way since the time when traditional sequencing techniques required many labs around the world to cooerate for over a decade, in order to sequence the human genome for the first time. Nowadays, high-throughut Sequencing By Synthesis technologies have reduced the task of sequencing a whole genome to a matter of days or even hours, and the cost has decreased by orders of magnitude, making it an accessible exerimental rocedure to many labs [27]. This oened the door for re-sequencing to start becoming a more routine rocedure, as it finds many alications in the detection of genetic variability among individuals. Thus, it can hel us understand the extent of that variability, and also identify secific variants, alternative slicing sites and atterns, eigenetic effects, and relate them to gene regulation and exression, as well as to diseases ([1], [28], [29], [19]). Thus, DNA sequencing is quickly becoming a owerful tool in diagnostic medicine, and eventually ersonalized treatment [27]. The data resulting from a single sequencing exeriment can be quite large, and it is not uncommon to have data from multile exeriments. This trend of increasing availability of sequencing data will continue as rojects even more ambitious than the 1000 Genomes Project [1] start to materialize. According to their resective websites, tyical outut sizes for the three main next-generation sequencing latforms are: over a million 400b-long reads er 10-hour run for the 454/Roche latform [3], u to 300GB er run for the ABI SOLiD latform [2], and u to 500 millions aired-end reads 100b-long for the Illumina GA [4]. In most cases these reads are too short to be directly assembled, esecially in the resence of reetitive regions [18], therefore a reference sequence is usually required. In the case of human genome re-sequencing, the reference genome is aroximately 3Gb-long. However, attemts to directly assemble short reads from simler genomes have begun [25], and a first attemt for human data has also been recently reorted [17]. Maing so many short reads onto such a long reference sequence is a very challenging task that cannot be adequately carried out by traditional search and alignment algorithms [11] like BLAST [5] and FASTA [20], so a broad array of rograms have been ublished to address this task, lacing emhasis on different asects of the challenge. The different algorithms imlement various combinations of innovations and trade-offs, to address comuting seed, system resources requirements, and biological relevance and accuracy of the comuted results. The need for more efficient ways to ma large numbers of short sequences was first acknowledged in 2002 and involved modifying the BLAST [5] algorithm so as to index the reference instead of the queries [11]. But really fast and efficient maing software started with ELAND [8], which is the software bundled in the Illumina GA ieline, and with constant develoment to match the advances of the

3 PARALLEL ALGORITHMS FOR MAPPING SHORT DEGENERATE AND WEIGHTED SEQUENCES 3 Illumina latform, it is still one of the fastest algorithms. MAQ [14] was released as an indeendent alternative to ELAND. It makes use of base-calling qualities and introduced maing qualities, but cannot do gaed alignment, and has an uer limit to the length of reads it can ma. Indexing the reads also otentially imoses a high demand on system resources, limiting the scalability of the method. SOAP [15] indexes the reference for more efficient memory usage and offers some form of gaed alignment, while SeqMa [10] allows more flexibility for gas and substitutions. Bowtie [12], SOAP2 [16] and BWA [13] (the successor of MAQ) make use of the Burrows-Wheeler Transform [7] to index the reference, and are able to achieve very good seed and relatively low memory usage. A number of other tools exist as well (REAL [9], SHRiMP [21], GSNAP [28]), each combining solutions differently and to different extents. Many of these alications show the necessity for a measure of accuracy concerning the maing methods. Accuracy can be quantified in terms of sensitivity and secificity. Possible causes of limitations in the accuracy of these exeriments include sequencing errors, variation between the samle and the reference genome, as well as ambiguities caused by reeats in the reference genome [26]. Therefore, the limitations of the equiment used, or the natural olymorhisms that can be observed between individual samles, can give rise to uncertain sequences. These uncertain sequences are called degenerate or indeterminate. Every entry in a degenerate string is a subset of the given alhabet. Very often, each osition of a sequence is accomanied by robabilities of each symbol occurring in the secific osition. In the case of the high-throughut exeriments, the base-calling qualities, which accomany the raw sequence data, describe the confidence of bases in each read [26]. The sequencing base-calling qualities assign a robability to the four ossible nucleotides for each sequenced base. Bases with low quality are more likely to be sequencing errors. These sequences, where the robability of every symbol s occurrence at every location is given, are called weighted sequences. In this aer, we design arallel algorithms for addressing the roblem of efficiently maing millions of short degenerate and weighted DNA sequences to a reference genome. The roosed arallel algorithms make use of the messageassing aradigm, and resemble the sequential strategies resented in [6] and [9]. Our aroach distributes the genomic sequence among the available rocessors, and rerocesses it, by using word-level arallelism and arallel sorting. Then, we distribute the queries among the available rocessors, and use the igeonhole rincile, binary search, and simle word-level oerations to seedu the maing rocess. The rest of the aer is organised as follows. In Section 2, the basic definitions that are used throughout the aer are resented. Section 3 formally defines the roblems solved in this aer. Section 4 and Section 5 resent the roosed algorithms for exact and aroximate matching, resectively. Finally, we briefly conclude with some future roosals in Section 6.

4 4 COSTAS S. ILIOPOULOS, MIRKA MILLER, SOLON P. PISSIS 2. Preliminaries A string is a sequence of zero or more symbols from an alhabet Σ. In this work, we are considering the finite alhabet Σ for DNA sequences, where Σ = {A, C, G, T }. The length of a string x is denoted by x. The i-th symbol of a string x is denoted by x[i]. A string w is a factor of x if x = uwv, where u, v Σ. We denote by x[i..j] the factor of x that starts at osition i and ends at osition j. In a string x on an alhabet Σ, a osition i is said to be degenerate or indeterminate iff x[i] may be any one of a secified subset {λ 1, λ 2,..., λ j } of Σ, 2 j Σ, and x[i] itself is said to be a degenerate symbol. If x[i] is a one-element subset it is called solid, non-solid otherwise. A string that may contain degenerate symbols is said to be degenerate (or indeterminate). For two strings x and y, such that only y is degenerate and x = y, the Hamming distance δ H (x, y) is the number of laces in which x[i] / y[i]. Formally, δ H (x, y) = x i=1 1 x[i] / y[i], where 1 x[i]/ y[i] = 1, if x[i] / y[i], or 0, otherwise. A weighted string over alhabet Σ is a sequence x = x[1..n] of sets of airs. In articular, each x[i] is a set of airs ((q 1, π i (q 1 )), (q 2, π i (q 2 )),..., (q Σ, π i (q Σ )), where π i (q j ) is the occurrence robability of symbol q j at osition i. A symbol q j occurs at osition i of a weighted sequence x = x[1..n] iff the robability of occurrence of symbol q j at osition i is greater than zero, i.e. π i (q j ) > 0. For every osition 1 i n, Σ j=1 π i(q j ) = 1. For examle, ( A 0.8 C 0.2) is a non-solid symbol, imlying that base A occurs with robability 80% and C with robability 20%. The roosed arallel algorithms make use of the message-assing aradigm, by using rocessing elements. The following assumtions for the model of communications in the arallel comuter are made. The arallel comuter comrises a number of nodes. Each node comrises one or several identical rocessors interconnected by a switched communication network. The time taken to send a message of size n between any two nodes is indeendent of the distance between nodes and can be modeled as t comm = t s + nt w, where t s is the latency or start-u time of the message, and t w is the transfer time er data. The links between two nodes are full-dulex and single-orted: a message can be transferred in both directions by the link at the same time, and only one message can be sent and one message can be received at the same time. 3. Problems definition We denote the generated short sequences as the set 1, 2,..., r, where r is a natural number (r > 10 7 in ractice), and we call them atterns. The length of each attern is currently, tyically between 25 and 75 b long. Without loss of generality, we denote the length of the atterns as l. We assume that the data is derived from high-quality sequencing methods, and therefore we will only consider degenerate or weighted atterns with at most µ l non-solid symbols. The given text is a genomic sequence t = t[1..n], where n > 10 8, and we are also given a ositive threshold k 0.

5 PARALLEL ALGORITHMS FOR MAPPING SHORT DEGENERATE AND WEIGHTED SEQUENCES 5 We formally define the roblem of maing short degenerate and weighted sequences to a reference genome, as follows. Problem 1. Find whether the degenerate attern i = i [1..l], for all 0 i < r, with at most µ non-solid symbols, occurs with at most k-mismatches in text t = t[1..n]. Problem 2. Find whether the weighted attern i = i [1..l], for all 0 i < r, with at most µ non-solid symbols, occurs with at most k-mismatches in text t = t[1..n], with robability at least γ, if l i=1 π i(q j ) γ, q j Σ, 1 j Σ. The case that k > 0 corresonds to the ossibility that the attern either contains a sequencing error, or a small difference between a mutant and the reference genome. 4. Exact Pattern Matching In this section, the focus is to find all the occurrences of a degenerate or a weighted attern i, for all 0 i < r, in text t = t[1..n], with no mismatches, i.e. k = 0. In order for the rocedure to be efficient, each rocessor makes use of word-level arallelism by transforming each factor of length l of t into a signature. We get the signature σ(x) of a string x, by transforming it to its binary equivalent using 2-bits-er-base encoding of the DNA alhabet, and storing its decimal value into a comuter word. For simlicity, we assume that the signature fits in the comuter word, i.e. 2l w, where w is the word size of the machine (e.g. 32 or 64 in ractice). Notice that, in the case that 2l > w, the roosed algorithm can easily be adoted by storing the signatures in 2l/w comuter words. Our aim is to rerocess the text t and create a local list L on each rocessor. List L holds elements of tye e i =(i, σ(z i )), where i reresents the starting osition of factor z i = t[i... i + l 1]. An outline of Algorithm I is as follows. Problem Partitioning. We use a data decomosition aroach to artition the text t with the sliding window mechanism into a set of factors z 1, z 2,..., z n l+1 of length l, where z i = t[i... i + l 1], for all 1 i n l + 1. Ste 1. We assume that text t is stored locally on the master rocessor. We make sure that the load is evenly balanced by distributing the factors of t among the available rocessors. Without loss of generality, we denote as z firstρ,..., z lastρ the set of the allocated factors of rocessor ρ, for all 0 ρ <. Ste 2. Each rocessor ρ, for all 0 ρ <, transforms each allocated factor z i, for all first ρ i last ρ, into a signature σ(z i ), acks it in an element e i =(i, σ(z i )),

6 6 COSTAS S. ILIOPOULOS, MIRKA MILLER, SOLON P. PISSIS and adds e i to a local list Z ρ. As soon as rocessor ρ comutes σ(z firstρ ), then each σ(z i ), for all first ρ + 1 i last ρ, can be retrieved in constant time (using shift -tye oerations). Ste 3. We sort the elements of the local lists Z ρ, for all 0 ρ <, based on the signature s field in arallel, using Parallel Sorting by Regular Samling (PSRS) [24], a ractical arallel sorting algorithm. Notice that arallel sorting means rearranging the elements of the local lists Z ρ, so that each rocessor ρ still has an evenly balanced amount of elements in Z ρ, but the elements are stored in sorted order by rocessor 0, 1,..., 1. Ste 4. We erform a gather oeration, in which the master rocessor collects, the local list Z ρ, from each other rocessor, and stores each local list Z ρ in rank order, resulting in a new combined sorted list L, i.e. σ(x) L[i] σ(y) L[i + 1], for all 1 i n l. The master rocessor erforms a one-to-all broadcast to send L to all other rocessors. Ste 5. We make sure that each rocessor is allocated an evenly balanced amount of query atterns from the set 1, 2,..., r. Assume that we have a degenerate query i [1..l], 1 i r. Let i = i [1] i [2]... i [l] (1) the Cartesian roduct. For each g i i, 1 g Σ µ, we can comute signature σ( g i ). Thus, we extend the set of atterns 1, 2,..., r, to a new set X = { g i : 1 i r, 1 g Σ µ }, where X Σ µ r. In addition to that, if i is a weighted attern (Problem 2), we must check that l i=1 π i(q j ) γ, q j Σ, 1 j Σ, is satisfied. Then, we can easily check whether i occurs in t by using binary search. If there exists a attern g i, such that g i i and σ( g i ) L, then i occurs in t. Theorem 1. Algorithm I solves Problem 1 and Problem 2 for k = 0, in O( n log n + Σ µ r log n) comutation time and O(n log + r) communication time. Proof. In ste 1, assuming that the text t is ket locally on the master rocessor, the distribution of t among the available rocessors can be done in O(t s log + ( 1)) communication time. In ste 2, each rocessor creates an evenly balanced amount of signatures of the factors of t in O( n ) comutation time. In ste 3, the PSRS algorithm can be executed in O( n log n ) comutation time, where n 3, and O(n/ ) communication time [24]. In ste 4, the gather oeration can be done n in O(t s log + t w ( 1)), and the one-to-all broadcast takes O((t s + t w n) log ) t w n communication time. Ste 5 runs in O( Σ µ r search, and O(t s log + t w r log n) comutation time, for the binary ( 1)) communication time, for the distribution of the atterns. Hence, asymtotically, the overall time is O( n log n + Σ µ r log n)

7 PARALLEL ALGORITHMS FOR MAPPING SHORT DEGENERATE AND WEIGHTED SEQUENCES 7 comutation time, which is O( n log n + r log n) in ractice, and O(n log + r) communication time. 5. Aroximate Pattern Matching In this section, the focus is to find the occurrences of i, for all 0 i < r, in text t = t[1..n] with at most k-mismatches, i.e. k 0. Here, the idea of using the igeonhole rincile to slit each signature into ν fragments is adoted. By requiring some of the ν fragments (instead of all of them) to be erfectly matched, the noncandidates can be filtered out very quickly. For examle, to admit two mismatches, a attern can be slit into four fragments. The two mismatches can exist in at most two of the fragments (at the same time). Then, if we try all six combinations of the two fragments as the seed, we can catch all hits with two mismatches. Lemma 2. Given the number of fragments ν of a string x = {x 1, x 2,..., x ν }, and the number of allowed mismatches k, k < ν, any of the k mismatches cannot exist, at the same time, in at least ν k fragments of x. Proof. Immediate from the igeonhole rincile. Without loss of generality, we choose ν, such that ν k = k and 2l/ν w, where w is the size of the comuter word. We denote as c j (σ(x)) = {σ(x a 1 ), σ(x a 2 ),..., σ(x a ν k )}, with a 1 < a 2 <... < a ν k, the ( ν combinations of σ(x) = {σ(x 1 ), σ(x 2 ),..., σ(x ν )}, such that if c j+1 = {σ(x b 1 ), σ(x b 2 ),..., σ(x b ν k )}, then ν k i=1 a i ν k i=1 b i, for all 1 j < ( ν. We denote as d q (σ(x)) = {σ(x a1 ), σ(x a2 ),..., σ(x a k )}, with a 1 < a 2 <... < a k, the rest k fragments of σ(x), such that if d q+1 = {σ(x b1 ), σ(x b2 ),..., σ(x b k )}, then k i=1 a i k i=1 b i, for all 1 q < ( ν. Our aim is to rerocess the text t and construct ( ν local lists Lj, for all 1 j ( ν on each rocessor. Each list Lj holds elements of tye e j i = (i, sj i, nextj i ), where i reresents the starting osition of factor z i = t[i... i + l 1], s j i is the concatenated fragments of c j (σ(z i )), and next j i oints to eq i = (i, sq i, nextq i ), where s q i the rest concatenated fragments of d q(σ(z i )) of σ(z i ), in L q. We define the following oerations: f(j): a function that given j, it returns q, such that if c j (σ(x)) = {σ(x a1 ), σ(x a2 ),..., σ(x a ν k )} and d q (σ(x)) = {σ(x b 1 ), σ(x b 2 ),..., σ(x b k )}, then

8 8 COSTAS S. ILIOPOULOS, MIRKA MILLER, SOLON P. PISSIS c j d q = {σ(x 1 ), σ(x 2 ),..., σ(x ν )}, for some string x. h(c i (σ(x))): a function that given c i (σ(x)), it returns s, the concatenated fragments of c i (σ(x)), for some string x. bs(s, L j ): a binary search oeration that given a signature s and the list L j, it returns {e j a 1, e j a 2,..., e j a v } such that s e j a i, for all 1 i v. bito(σ(x), σ(y)): a word level oeration that given two strings x and y, with x = y = α and 2α w, where w is the size of the comuter word, it returns δ H (x, y), in constant time. An outline of Algorithm II is as follows. Problem Partitioning. We use a data decomosition aroach to artition the text t with the sliding window mechanism into a set of factors z 1, z 2,..., z n l+1 of length l, where z i = t[i... i + l 1], for all 1 i n l + 1. Ste 1. We assume that text t is stored locally on the master rocessor. We make sure that the load is evenly balanced by distributing the factors of t among the available rocessors. Without loss of generality, we denote as z firstρ,..., z lastρ the set of the allocated factors of rocessor ρ, for all 0 ρ <. Ste 2. Each rocessor ρ, for all 0 ρ <, comutes σ(z i ), for all first ρ i last ρ. Then, it comutes c j (σ(z i )), q = f(j), d q (σ(z i )), for all 1 j ( ν /2, and add e j i = (i, h(c j(σ(z i )), i) and e q i = (i, h(d q(σ(z i )), i) to the local lists Zρ j and Zρ, q resectively. In this way, we construct ( ) ν ν k local lists Z j ρ, for all 1 j ( ν, on each rocessor ρ, for all 0 ρ <. Ste 3. We sort the elements of the local lists Z j ρ, for all 1 j ( ν, for all 0 ρ <, based on the signature s field, in arallel, using PSRS, ensuring that, in the case that we swa elements, we reserve that next j i still oints to eq i and nextq i oints to e j i. Ste 4. We erform a gather oeration, in which the master rocessor collects the local lists Zρ, j for all 1 j ( ν, from each other rocessor, and stores each local list Zρ j in rank order, resulting in a new combined sorted list L j, for all 1 j ( ν. The master rocessor erforms a one-to-all broadcast to send Lj to all other rocessors. Ste 5. We make sure that each rocessor is allocated an evenly balanced amount of query atterns from the set 1, 2,..., r. Assume that we have a degenerate query i [1..l], 1 i r. Let i = i [1] i [2]... i [l] (2)

9 PARALLEL ALGORITHMS FOR MAPPING SHORT DEGENERATE AND WEIGHTED SEQUENCES 9 the Cartesian roduct. For each g i i, 1 g Σ µ, we can comute signature σ( g i ). Thus, we extend the set of atterns 1, 2,..., r, to a new set X = { g i : 1 i r, 1 g Σ µ }, where X Σ µ r. In addition to that, if i is a weighted attern (Problem 2), we must check that l i=1 π i(q j ) γ, q j Σ, 1 j Σ, is satisfied. We comute σ( g i ), c j(σ( g i )), q = f(j) and d q(σ( g i )), for all 1 j ( ν. Then, we erform the binary search oeration bs(h(cj (σ( g i ))), L j), which returns {e j a 1, e j a 2,..., e j a v }. If there exists e j a λ, for some 1 λ v, such that bito(h(d q (σ( g i ))), sq a λ ) k and s q a λ e j a λ, then i occurs in t with at most k- mismatches. Theorem 3. Algorithm II solves Problem 1 and Problem 2 in O(ν n log n + Σ µ r ( ν log n) comutation time, and O(νn log + r) communication time. Proof. In ste 1, assuming that the text t is ket locally on the master rocessor, the distribution of t among the available rocessors can be done in n O(t s log + t w ( 1)) communication time. In ste 2, each rocessor creates an evenly balanced amount of signatures of the factors of t in O(ν n ) comutation time. In ste 3, the PSRS algorithm can be executed in O(ν n log n ) comutation time, where n 3, and O(n/ ) communication time. In ste 4, the gather oeration can be done in O(t s log + t w ν n ( 1)), and the one-to-all broadcast take O((t s +t w νn) log ) communication time. Ste 5 runs in O( Σ µ r ( ν log n) comutation time, for the binary search, and O(t s log +t w r ( 1)) communication time, for the atterns distribution. Hence, asymtotically, the overall time is O(ν n log n + Σ µ r ( ν ) ν k log n) comutation time, which is O(ν n log n + ( r ν log n) in ractice, and O(νn log + r) communication time. 6. Conclusion In this aer, we have resented arallel algorithms to tackle the data emerging from the next-generation sequencing technologies. These new technologies roduce a huge number of very short sequences, and these sequences need to be classified, tagged and recognised as arts of a reference genome. Very often, these sequences either contain degenerate symbols, or they are accomanied by the occurrence robability of each symbol at each osition of the sequence. To the best knowledge of the authors, the resented algorithms is the first roosed aroach, which makes use of the message-assing arallelism model, for the roblem of maing these sequences to a reference genome. In articular, we have resented Algorithm I for exact matching. It runs log n) comutation time, and O(n log + r) communication time, where is the number of available rocessors, n is the length of the genomic sequence, r is the number of atterns, Σ is the DNA alhabet, and µ is the maximum number of non-solid symbols of a attern. In addition, we have resented Algorithm II for aroximate matching. It in O( n log n + Σ µ r

10 10 COSTAS S. ILIOPOULOS, MIRKA MILLER, SOLON P. PISSIS runs in O(ν n log n + Σ µ r ( ν log n) comutation time, and O(νn log + r) communication time, where ν is the number of equal length fragments into which each attern is slit, and k is the number of allowed mismatches. The sequential versions of Algorithm I and Algorithm II were imlemented on a real dataset and resented in [6] and [9], giving some very romising results comaring to more traditional aroaches. Our immediate target is to build a software tool, which will be based on the resented algorithms, and will be used by the biologists for maing short sequences to a reference genome. References [1] htt:// [2] htt://www3.aliedbiosystems.com. [3] htt:// [4] htt:// [5] S. F. Altschul, W. Gish, W. Miller, E. W. Myers, and D. J. Liman. Basic Local Alignment Search Tool. Journal of Molecular Biology, 215(3): , October [6] P. Antoniou, C. S. Iliooulos, L. Mouchard, and S. P. Pissis. Algorithms for maing short degenerate and weighted sequences to a reference genome. Int. J. Comutational Biology and Drug Design, 2(4): , [7] M. Burrows and D. Wheeler. A block sorting lossless data comression algorithm. Digital Equiment Cororation, Technical Reort 124, [8] A. Cox. ELAND, unublished [9] K. Frousios, C. S. Iliooulos, L. Mouchard, S. P. Pissis, and G. Tischler. REAL: An efficient REad ALigner for next generation sequencing reads. In Proceedings of the 1st International Conference On Bioinformatics and Comutational Biology (ACM-BCB 2010), (in ress). [10] H. Jiang and W. H. Wong. SeqMa: maing massive amount of oligonucleotides to the genome. Bioinformatics, 24(20): , [11] W. J. Kent. BLAT - the BLAST -like alignment tool. Genome Research, 12: , [12] B. Langmead, C. Tranell, M. Po, and S. L. Salzberg. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology, 10(3):R25. [13] H. Li and R. Durbin. Fast and accurate short read alignment with Burrow-Wheeler transform. Bioinformatics, 25(14): , [14] H. Li, J. Ruan, and R. Durbin. Maing short DNA sequencing reads and calling variants using maing quality scores. Genome Research, 18: , [15] R. Li, Y. Li, K. Kristiansen, and J. Wang. SOAP: short oligonucleotide alignment rogram. Bioinformatics, 24(5): , [16] R. Li, C. Yu, Y. Li, T.-W. Lam, S.-M. Yiu, K. Kristiansen, and J. Wang. SOAP2 : an imroved ultrafast tool for short read alignment. Bioinformatics, 25(16): , [17] R. Li, H. Zhu, J. Ruan, W. Qian, X. Fang, Z. Shi, Y. Li, S. Li, G. Shan, K. Kristiansen, S. Li, H. Yang, J. Wang, and J. Wang. De novo assembly of human genomes with massively arallel short read sequencing. Genome Research, 20(2): , February [18] J. R. Miller, S. Koren, and G. Sutton. Assembly algorithms for next-generation sequencing data. Genomics, doi: /j.ygeno [19] S. B. Ng, K. J. Buckingham, C. Lee, A. W. Bigham, H. K. Tabor, K. M. Dent,

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