SeqAn An efficient, generic C++ library for sequence analysis
© Döring et al; licensee BioMed Central Ltd. 2008
Received: 21 August 2007
Accepted: 09 January 2008
Published: 09 January 2008
The use of novel algorithmic techniques is pivotal to many important problems in life science. For example the sequencing of the human genome  would not have been possible without advanced assembly algorithms. However, owing to the high speed of technological progress and the urgent need for bioinformatics tools, there is a widening gap between state-of-the-art algorithmic techniques and the actual algorithmic components of tools that are in widespread use.
To remedy this trend we propose the use of SeqAn, a library of efficient data types and algorithms for sequence analysis in computational biology. SeqAn comprises implementations of existing, practical state-of-the-art algorithmic components to provide a sound basis for algorithm testing and development. In this paper we describe the design and content of SeqAn and demonstrate its use by giving two examples. In the first example we show an application of SeqAn as an experimental platform by comparing different exact string matching algorithms. The second example is a simple version of the well-known MUMmer tool rewritten in SeqAn. Results indicate that our implementation is very efficient and versatile to use.
We anticipate that SeqAn greatly simplifies the rapid development of new bioinformatics tools by providing a collection of readily usable, well-designed algorithmic components which are fundamental for the field of sequence analysis. This leverages not only the implementation of new algorithms, but also enables a sound analysis and comparison of existing algorithms.
In other fields, software libraries have greatly advanced the transfer of algorithmic knowledge to the tool programming process. Two of the best known examples are the LEDA library  for algorithms on graphs and efficient data types and the CGAL library [12, 13] for computational geometry. In bioinformatics, a comparable library is still missing although there is a need for integrated implementations of algorithms for aligning sequences, computing substring indices in primary and secondary memory, or filter algorithms. In addition, a library that adheres to the principles of algorithm engineering is essential as a means to test and compare existing tools as well as to evaluate the results from algorithmic research. The lack of such a library becomes evident when reviewing the related work of the past years.
A few C++ libraries with sequence analysis features have already been developed, including Bio++ , Libcov , the Bioinformatics Template Library (BTL) , the NCBI C++ Toolkit , or the Sequence Class Library (SCL) . Bio++ is the most comprehensive library providing re-usable components for phylogenetics, molecular evolution, and population genetics. The sequence analysis part is, however, limited to basic import/export capabilities and string manipulations. In contrast to SeqAn, which is based upon the generic programming paradigm, Bio++ is a purely object-oriented library, favoring ease of development over performance and scalability. Libcov focusses on phylogenetics and clustering algorithms. It offers only basic data structures to handle sets of sequences. Alignment algorithms, database indices, or scoring matrices are not provided. The BTL emphasizes basic mathematical algorithms and data structures. It currently comprises graph classes and linear algebra algorithms but only a single sequence alignment algorithm, Needleman-Wunsch  with cubic running time. The NCBI C++ Toolkit also offers, beside other things, some sequence analysis functionality, e.g. alignment algorithms. The SCL, providing some basic sequence analysis components, is to our knowledge not activly developed anymore.
Besides these C++ libraries, we are aware of alternative approaches like BioPerl  or BioJava . The main purpose of BioPerl is to ease the development of sequence analysis pipelines by providing an interface to already existing tools. BioJava on the other hand is suited for developing new sequence analysis tools by providing many relevant data structures and algorithms and as such is from the overall goals perhaps closest to SeqAn. Some algorithms are shared by both libraries (like Needleman-Wunsch and Smith Waterman). A closer inspection, however, reveals that BioJava does only offer a small part of SeqAn's functionality (no indices, no algorithms for de novo motif search, no algorithms for multiple alignment, etc.). Hence both libraries are in this sense complementary. In addition, we show in the result section that our implementations are for standard alignment problems by a factor of 6 to 350 times faster and by a factor of 600 to 1500 times more space efficient.
The exposition is structured as follows: To emphasize the usefulness of SeqAn, this article centers around the contents of the library, described in Section and the practical application of SeqAn, exemplified in Section. In the following section we start by giving a brief outline of the design principles SeqAn is based on.
For developing the basic design, SeqAn has gone through an extensive conceptual phase in which we evaluated many designs and prototypic implementations. SeqAn has now a generic programming design that guarantees high performance, generality, extensibility, simplicity, and easy integration with other libraries. This design is based on four design principles which we will describe now.
SeqAn adopts the generic programming paradigm that proved to be a key technique for achieving high performance algorithms in the C++ standard library . Generic programming refers to a special style of programming where concrete types are substituted by exchangeable template types. Hence, classes and algorithms are written only once, but can be applied to different data types.
Global Function Interfaces
SeqAn uses global functions instead of member functions to access objects (we act here on an advice of , see Section 6.10.2.). This strategy improves the flexibility and the scalability of our library, since global functions, unlike member functions, can be added to a program at any time and without changing the existing code. Moreover, global function interfaces enable us to incorporate the C++ built-in types and handle them like user defined types. It is even possible to adapt arbitrary interfaces, i.e. of classes that are implemented in external libraries, to a common interface by using small global functions called 'shims' (Chapter 20 in ). Algorithms that access objects only via global functions can therefore be applied to a great variety of types, including built-in types and external classes.
Generic algorithms usually have to know certain types that correspond to their arguments: An algorithm on strings may need to know which type of characters are stored in the string, or what kind of iterator can be used to browse it. SeqAn uses type traits  for that purpose. In C++, trait classes are implemented as class templates that map types or constants given by template arguments to other types but also other C++ enties like constants, functions, or objects at compile time. Most of the advantages we already stated for global functions also apply to traits, i.e. new traits and new specializations of already existing traits can be added without changing other parts of the library.
Template Argument Subclassing
SeqAn uses a special kind of hierarchical structure that we call 'template argument subclassing', which means that different specializations of a given class template are specified by template arguments. For example, String<Compressed> is a subclass of String in the sense that all functions and traits which are applicable to String can also be applied to String<Compressed>, while it is possible to overload some functions especially for String<Compressed>. The rules of C++ overload resolution guarantee that the compiler always applies the most specific variant out of all existing implementations when an algorithm or trait has been called. This approach resembles class derivation in standard object-oriented programming, but it is often faster, because it does not require a type conversion for a subclass calling a function that is already defined for the base class, and since the actual type of the object used in a function is therefore already known at compile time, it is not necessary to detect it at run time using virtual functions. Non-virtual functions have the advantage that C++ compilers can use function inlining to save their overhead completely. Template argument subclassing enables us both to specialize functions and to delegate tasks soundly to base classes while still maintaining static binding.
These design principles support our design goals in the following way:
Performance: The library produces code that is competitive with manually optimized programs. Template argument subclassing makes it possible to plug in optimized specializations for algorithms whenever needed. Our generic programming design also speeds up the code in avoiding unnecessary virtual function calls.
Generality: All parts of the library are as flexible as possible. Algorithms can be applied to various data types and new types can be added if necessary. For example, generic alignment algorithms in SeqAn work on strings for arbitrary alphabets. However, specialized implementations that make use of certain attributes of the alphabet can still be developed using template argument subclassing.
Integration: SeqAn components are designed to fulfill the requirements specified in the C++ standard. In addition, SeqAn easily interacts with other libraries because the global interface can be expanded. Hence, algorithms and classes of other libraries are at hand.
Extensibility: The open-closed principle ('Be open for extension but closed for modifications!') is satisfied in so far as it is possible to extend the library by simply adding new code. SeqAn has this feature because it relies on stand-alone global functions and traits that can be added at any time without changing the existing code.
Simplicity: While a pure object-oriented library may be more familiar to some users, SeqAn is still simple enough to be used even by developers with average skills in C++.
The storage and manipulation of sequences is essential for all algorithms in the field of sequence analysis. In SeqAn, sequences are represented as strings of characters over various alphabets. Multiple string classes for different settings are available: Large sequences can be stored in secondary memory using external strings, bit-packed strings can be used to take advantage of small alphabets, or strings allocated on the stack can be used to guarantee fast access. String modifiers can be used to implement distinct views on a given sequence without copying it. A string segment, for instance, is a string modifier used to get access to an infix, suffix, or prefix of a given sequence.
Alignments require the insertion of gaps into sequences. SeqAn does not actually insert these gaps directly into the sequence but treats them separately. The benefit is twofold: A single sequence can be used in multiple alignments simultaneously and the actual alphabet of the string must not include a special gap character. SeqAn offers both pairwise and multiple sequence alignment algorithms. Algorithms can be configured for different scoring schemes and different treatments of sequence ends (e.g, ends free-space alignments). In the pairwise case, local and global alignment algorithm are available. Besides the classical Needleman-Wunsch algorithm , more sophisticated algorithms are available, including an affine gap cost alignment  and Myer's bit vector algorithm . Moreover, SeqAn offers efficient algorithms to chain alignment fragments [27, 28]. We are also currently integrating code for motif finding in multiple sequences.
The enhanced suffix array (ESA) is probably the most fundamental indexing data structure in bioinformatics with various applications, e.g., finding maximal repeats, super maximal repeats, or maximal unique matches in sequences. An enhanced suffix array is a normal suffix array extended with an additional lcp table that stores the length of the longest common prefix of adjacent suffixes in the suffix array. SeqAn offers an ESA that can be build up in primary or in secondary memory, depending on the sequence size. The user has two choices to access the ESA, either as a regular suffix array or as a suffix tree. The later view on an ESA is realized using the concept of iterators that simulate a tree traversal. A more space and time efficient data structure for top-down traversals through only parts of the suffix tree is the lazy suffix tree  which is also implemented in SeqAn. Besides the sophisticated ESA, simpler indices are available, including basic hash tables like gapped- and ungapped q-gram indices (for their use see [31–33]).
Flexible pattern matching algorithms are fundamental to sequence analysis. Exact and approximate string matching algorithms are provided. For the exact string matching task, SeqAn offers the algorithms Shift-And, Shift-Or, Horspool, Backward Oracle Matching, and Backward Nondeterministic Dawg Machine . For searching multiple patterns, SeqAn currently supports the Multiple Shift-And, the Set Horspool, and the Aho-Corasick algorithm . Myer's bit vector algorithm  can be used for approximate string matching. Note that SeqAn's index data structures can naturally be used to search for strings as well.
Graphs are increasingly important to a number of bioinformatics problems. Prime examples are string matching algorithms (e.g., Aho-Corasick, Backward Oracle Matching ), phylogenetic algorithms (e.g., upgma, neighbor joining tree ), or alignment representations . Hence, we decided to include our own graph type implementation, including directed graphs, undirected graphs, trees, automata, alignment graphs, tries, wordgraphs, and oracles. Graph algorithms currently comprise breath-first search, depth-first search, topological sort, strongly-connected components, minimum spanning trees (e.g., Prim's algorithm, Kruskal's algorithm), shortest path algorithms (e.g., Bellman-Ford, Dijkstra, Floyd-Warshall), transitive closure, and the Ford-Fulkerson maximum flow algorithm . Trees are heavily used in clustering algorithms and as guide trees during a progressive multiple sequence alignment. Alignment graphs are used to implement a heuristic multiple sequence alignment algorithm, which is similar to T-Coffee  but makes use of segments and a sophisticated refinement algorithm  to enable large-scale sequence alignments.
Besides the fundamental alphabets for biological purposes, like DNA or amino acids, SeqAn offers different scoring schemes for evaluating the distance of two characters, e.g., PAM, and BLOSUM. SeqAn also supports several file formats that are common in the field of bioinformatics, e.g., FASTA, EMBL, and genbank. Is is possible the access (e.g. to search) sequence data stored in such file formats without loading the whole data into memory. The integration of external tools (e.g., BLAST) and the parsing of metainformation is ongoing work.
We anticipate two different user groups for SeqAn. The first group is the bioinformatics practitioner with some programming knowledge who wants to quickly prototype efficient tools for analyzing genomic or protein sequences using SeqAn. The other prototypic user is the algorithmicist who is proficient in programming in SeqAn and wants to test and compare an algorithmic component for a specific well-defined algorithmic problem.
The next examples will demonstrate how things could be done in SeqAn. We would like to point out the very good performance of SeqAn as well as the fact that the necessary code is small, easy to understand, generic, and greatly profits from using an integrated algorithmic library.
Example: String Matching
Example: Global Alignments
Now we switch to a more biologically motivated example: Computing a global alignment between two given DNA sequences with minimal edit distance. Alignment problems are very popular in the biological context. Even libraries with little sequence analysis content support one or more relevant functions that are mostly based on the dynamic programming approach by Needleman and Wunsch , which is certainly one of the most popular algorithms in bioinformatics. Gotoh's algorithm  extends it by affine gap cost models. Some libraries also support Hirschberg's algorithm , another well-known alignment method that takes only linear space.
Runtimes and internal space requirements for computing sequence alignments. The table shows average time and space requirements for aligning the genomes of two human influenca viruses, each of length about 15.6 kbp. Runtimes printed in bold face show for each library the time of the fastest algorithm for computing an alignment using edit distance.
linear gap costs
affine gap costs
NCBI C++ toolkit
In this example, we want to convince the reader that programming using SeqAn is not difficult and that SeqAn is simple enough to meet the needs of the first user group while it is efficient and generic enough to allow expert users to use SeqAn as an experimental platform for testing algorithmic components.
We choose as an example the well-known MUMmer  tool and show in the listing (see Additional File 1) an implementation of a (simplified) version of the tool which reads a number of sequences and computes all maximal unique matches (MUMs) of length at least 20. For the sake of exposition we only show code pieces that are illustrative for SeqAn.
A MUM of a set of sequences is a subsequence that occurs exactly once in each sequence and that is not part of any longer such subsequence. To find MUMs MUMmer builds a suffix tree  of a reference sequence and streams one or more query sequences against it. The downside of designating one sequence as the reference is that matches are only unique in the reference sequence but not necessarily in the query sequence. To guarantee the uniqueness of a match in all sequences it is necessary to construct a generalized suffix tree. A generalized suffx tree is a suffix tree of the concatenated sequences seperated by unique characters . It is the primary index data structure in SeqAn and based on an enhanced suffix array . In the first part of the example (Additional File 1: Listing 1) we build a string index for a set of strings consisting of characters from the Dna5 alphabet, which is an extension of the Dna alphabet including the 'N' character. SeqAn supports a number of different alphabets of biological relevance (e.g., Dna, Amino Acid, or compressed amino acid alphabets). All these alphabets enable us to store sequences efficiently because of the reduced number of characters compared to normal text. The index is first resized to the appropriate number of sequences. Subsequently, the sequences are imported using the Fasta read function and simultaneously, these sequences are added to the index, which is our enhanced suffix array.
SeqAn provides iterators that make it possible to traverse the enhanced suffix array like a suffix tree in a bottom-up fashion. This is illustrated in Additional File 1: Listing 2. The iterator it visits each node u in the generalized suffix tree. To find a MUM u, it suffices to test whether u occurs exactly 2 times (line 16), at most once in each sequence (line 18), and cannot be extended to the left (line 19) (see Chapt. 3.4, ). If the length of the representative string of u is also at least 20 (line 17) we report the position and length of the MUM u (lines 26–31). Assuming a computational biologist is not all too interested in these algorithmic details but in performance and a simple interface, SeqAn provides specialized iterators to get all MUMs (Additional File 1: Listing 3), maximal or supermaximal repeats, or MultiMEMs ). Since performance is a crucial issue in any kind of sequence analysis task, we compared our code example with the latest MUMmer release  and Multimat of the MGA distribution . To the best of our knowledge these are the only tools to find MUMs. None of the libraries introduced in chapter support generalized suffix trees or even algorithms on suffix trees, like those to find MUMs. Our testset consisted of various bacteria strains and vertebrate chromosomes.
Runtimes and internal space requirements for finding MUMs. We compared MUMmer 3.19 , MGA , and SeqAn for different DNA sequences on a 3.2 GHz Intel Xeon computer with 3 GB of internal memory running Linux. Because MUMmer finds MUMs of not more than two sequences, its results on the Chlamydia and Escherichia coli strains are left empty. For the last dataset, we used SeqAn's external memory data strutures to limit the internal memory consumption.
C. trachomatis D/UW-3/CX
C. muridarum Nigg
C. trachomatis A/HAR-13
E. coli K12
E. coli O157:H7 str. Sakai
E. coli CFT073
E. coli UTI89
E. coli 536
E. coli APEC O1
H. sapiens (chr. 21)
M. musculus (chr. 16)
H. sapiens (chr. 16)
P. troglodytes (chr. 16)
H. sapiens (chr. 1)
M. musculus (chr. 1)
Index data structures of whole genomes easily reach 10–30 GB, so they must rely on external memory. SeqAn provides such data structures. They can be used by simply exchanging the standard string of SeqAn by an external memory string in order to construct the generalized suffix tree in external memory. We did this for the last row of Table 1 and simply replaced Dna5String by String<Dna5, External<>> in the code example. This reduces the main memory space requirements of the algorithm at the expense of speed. However, this makes it possible to construct generalized suffix trees for sequences of nearly arbitrary length. As can be seen in Table 1, these external strings enable SeqAn to handle long sequences where MUMmer and MGA simply run out of memory.
We presented a new software library with an efficient and generic design that addresses a wide range of problems in sequence analysis. SeqAn is under active development and we hope that it will become one of the standard platforms for algorithmic engineering at the interface of stringology, algorithm design and computational biology. Besides the planned extensions mentioned in Section, we are working on integrating external libraries and plan to intensify our collaborations with other research groups.
Availability and requirements
SeqAn is freely distributed under the GNU Lesser General Public Licence (LGPL), both for academic and non-academic use. The library and its documentation can be downloaded from http://www.seqan.de. All parts of the library are tested on Windows with Microsoft Visual Studio 2003 and 2005 and on Linux with G++ compilers version 3.0 and above.
We would like to acknowledge all students of the BSc and MSc program in bioinformatics at the FU Berlin who have contributed to SeqAn so far. Amongst others those are most notably Stephan Aiche, Anne-Katrin Emde, Ji-Hyun Lim, and Henrik Wöhrle.
- Venter JC, Reinert K, et al.: The Sequence of the Human Genome. Science 2001, 291: 1145–1434.View Article
- Myers EW: A fast bit-vector algorithm for approximate string matching based on dynamic programming. Journal of the ACM 1999, 46(3):395–415.View Article
- Altschul SF, Gish W, Miller W, Myers EW, Lipman DJ: Basic local alignment search tool. Journal of Molecular Biology 1990, 215: 403–410.View ArticlePubMed
- Manber U, Myers E: Suffix arrays: a new method for on-line string searches. In SODA'90: Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms. Society for Industrial and Applied Mathematics; 1990:319–327.
- Myers EW, Sutton GG, Delcher AL, Dew IM, Fasulo DP, Flanigan MJ, Kravitz SA, Mobarry CM, Reinert KHJ, Remington KA, Anson EL, Bolanos RA, Chou HH, Jordan CM, Halpern AL, Lonardi S, Beasley EM, Brandon RC, Chen L, Dunn PJ, Lai Z, Liang Y, Nusskern DR, Zhan M, Zhang Q, Zheng X, Rubin GM, Adams MD, Venter JC: A Whole-Genome Assembly of Drosophila. Science 2000, 287: 2196–2204.View ArticlePubMed
- Mural RJ, Adams MD, Myers GW, Reinert K, et al.: A Comparison of Whole-Genome Shotgun-Derived Mouse Chromosome 16 and the Human Genome. Science 2002, 296: 1661–1671.View ArticlePubMed
- Brudno M, Do C, Cooper GM, Kim MF, Davydov E, Program NCS, Green ED, Sidow A, Batzoglou S: LAGAN and Multi-LAGAN: Efficient Tools for Large-Scale Multiple Alignment of Genomic DNA. Genome Research 2003, 13(4):721–731.PubMed CentralView ArticlePubMed
- Kurtz S, Phillippy A, Delcher AL, Smoot M, Shumway M, Antonescu C, Salzberg SL: Versatile and open software for comparing large genomes. Genome Biology 2004, 5(2):R12.PubMed CentralView ArticlePubMed
- Höhl M, Kurtz S, Ohlebusch E: Efficient multiple genome alignment. ISMB (Supplement of Bioinformatics) 2002, 312–320.
- Darling A, Mau B, Blattner F, Perna N: Mauve: Multiple Alignment of Conserved Genomic Sequence with Rearrangements. Genome Research 2004, 14: 1394–1403.PubMed CentralView ArticlePubMed
- Mehlhorn K, Näher S: The LEDA Platform of Combinatorial and Geometric Computing. Cambridge University Press; 1999.
- Overmars MH: Designing the Computational Geometry Algorithms Library CGAL. Proceedings Workshop on Applied Computational Geometry 1996.
- Fabri A, Giezeman GJ, Kettner L, Schirra S, Schönherr S: The CGAL Kernel: A Basis for Geometric Computation. WACG: 1st Workshop on Applied Computational Geometry: Towards Geometric Engineering, WACG LNCS; 1996. [http://citeseer.ist.psu.edu/fabri96cgal.html]
- Dutheil J, Gaillard S, Bazin E, Glemin S, Ranwez V, Galtier N, Belkhir K: Bio++: a set of C++ libraries for sequence analysis, phylogenetics, molecular evolution and population genetics. BMC Bioinformatics 2006, 7: 188.PubMed CentralView ArticlePubMed
- Butt D, Roger AJ, Blouin C: libcov: A C++ bioinformatic library to manipulate protein structures, sequence alignments and phylogeny. BMC Bioinformatics 2005, 6: 138.PubMed CentralView ArticlePubMed
- Pitt WR, Williams MA, Steven M, Sweeney B, Bleasby AJ, Moss DS: The Bioinformatics Template Library – generic components for biocomputing. Bioinformatics 2001, 17(8):729–737.View ArticlePubMed
- Vakatov D, Siyan K, Ostell J, editors:The NCBI C++ Toolkit [Internet]. National Library of Medicine, National Center for Biotechnology Information, Bethesda (MD); 2003. [http://www.ncbi.nlm.nih.gov/books/bv.fcgi?rid=toolkit]
- Vahrson W, Hermann K, Kleffe J, Wittig B: Object-oriented sequence analysis: SCL-a C++ class library. Bioinformatics 1996, 12(2):119–127.View Article
- Needleman SB, Wunsch CD: A general method applicable to the search for similarities in the amino acid sequence of two proteins. J Molecular Biol 1970, 48: 443–453.View Article
- Stajich J, Block D, Boulez K, Brenner S, Chervitz S, Dagdigian C, Fuellen G, Gilbert J, Korf I, Lapp H, Lehvaslaiho H, Matsalla C, Mungall C, Osborne B, Pocock M, Schattner P, Senger M, Stein L, Stupka E, Wilkinson M, Birney E: The Bioperl toolkit: Perl modules for the life sciences. 2002.
- Pocock M, Down T, Hubbard T: BioJava: Open Source Components for Bioinformatics. ACM SIGBIO Newsletter 2000, 20(2):10–12.View Article
- Austern MH: Generic Programming and the STL. Addison Wesley; 1998.
- Czarnecki K, Eisenecker UW: Generative Programming. Methods, Tools, and Applications. Addison Wesley; 2000.
- Wilson M: Imperfect C++. Practical Solutions for Real-Life Programming. Addison Wesley; 2004.
- Vandevoorde D, Josuttis NM: C++ Templates. The Complete Guide. Addison Wesley; 2003.
- Gotoh O: An improved algorithm for matching biological sequences. J Mol Biol 1982, 162(3):705–708.View ArticlePubMed
- Abouelhoda M, Ohlebusch E: Chaining methods revisited. Proceedings of the 14th Annual Symposium on Combinatorial pattern matching (CPM) 2003 2003, 1–16.
- Myers G, Miller W: Chaining Multiple-Alignment Fragments in Sub-Quadratic Time. SODA: ACM-SIAM Symposium on Discrete Algorithms (A Conference on Theoretical and Experimental Analysis of Discrete Algorithms) 1995. [http://citeseer.ist.psu.edu/miller95chaining.html]
- Abouelhoda MI, Ohlebusch E, Kurtz S: Optimal Exact String Matching Based on Suffix Arrays. Proceedings of the Ninth International Symposium on String Processing and Information Retrieval, Lecture Notes in Computer Science 2476 Springer-Verlag; 2002, 31–43. [http://www.zbh.uni-hamburg.de/staff/kurtz/papers/AboOhlKur2002.pdf]
- Giegerich R, Kurtz S, Stoye J: Efficient Implementation of Lazy Suffix Trees. Software: Practice and Experience 2003, 33(11):1035–1049.
- Burkhardt S, Crauser A, Ferragina P, Lenhof HP, Rivals E, Vingron M: q-gram based database searching using suffix arrays. Proceedings of the third Annual International Conference on Computational Molecular Biology (RECOMB-99) 1999, 77–83.
- Burkhardt S, Kärkkäinen J: Better Filtering with Gapped q-grams. In CPM'01: Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching. London, UK: Springer-Verlag; 2001:73–85.View Article
- Li M, Ma B, Kisman D, Tromp J: PatternHunter II: Highly sensitive and fast homology search. Genome Informatics 2003, 14: 164–175.PubMed
- Navarro G, Raffinot M: Flexible Pattern Matching in Strings. CUP; 2002.View Article
- Saitou N, Nei M: The Neighbor-Joining method: a new method, for reconstructing phylogenetic trees. Mol Biol Evol 1987, 4: 406–425.PubMed
- Kececioglu J: The maximum weight trace problem in multiple sequence alignment. In Proc 4-th Symp Combinatorial Pattern Matching, no 684 in Lecture Notes in Computer Science. Springer-Verlag; 1993:106–119.View Article
- Cormen TH, Leiserson CE, Rivest RL, Stein C: Introduction to Algorithms. Cambridge, MA: MIT Press; 2001.
- Notredame C, Higgins D, Heringa J: T-Coffee: A Novel Method for Fast and Accurate Multiple Sequence Alignment. Journal of Molecular Biology 2000, 302: 205–217.View ArticlePubMed
- Halpern A, Huson D, Reinert K: Segment Match refinment and applications. Proceedings of the 2nd Workshop on Algorithms Bioinformatics (WABI-02) 2002, 126–139.View Article
- Hirschberg DS: A linear space algorithm for computing maximal common subsequences. Volume 18. ACM Press; 1975:341–343.
- Weiner P: Linear pattern matching algorithms. Proceedings of the 14th IEEE Symposium on Switching and Automata Theory 1973, 1–11.View Article
- Bieganski P, Riedl J, Carlis J: Generalized Suffix Trees for Biological Sequence Data: Applications and Implementation. Twentyseventh Annual Hawaii International Conference on System Sciences 1994.
- Abouelhoda M, Kurtz S, Ohlebusch E: Replacing Suffix Trees with Enhanced Suffix Arrays. Journal of Discrete Algorithms 2004, 2: 53–86. [http://www.zbh.uni-hamburg.de/staff/kurtz/papers/AboKurOhl2004.pdf]View Article
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