Suffix tree

Abstract: A new and conceptually simple data structure, called a suffix array, for on-line string searches is introduced in this paper. Constructing and querying suffix arrays is reduced to a sort and search paradigm that employs novel algorithms. The main advantage of suffix arrays over suffix trees is that, in practice, they use three to five times less space. From a complexity standpoint, suffix arrays permit on-line string searches of the type, “Is W a substring of A?” to be answered in time $O(P + \log N)$, where P is the length of W and N is the length of A, which is competitive with (and in some cases slightly better than) suffix trees. The only drawback is that in those instances where the underlying alphabet is finite and small, suffix trees can be constructed in $O(N)$ time in the worst case, versus $O(N\log N)$ time for suffix arrays. However, an augmented algorithm is given that, regardless of the alphabet size, constructs suffix arrays in $O(N)$expected time, albeit with lesser space efficiency. It is ...

Abstract: The MUMmer system and the genome sequence aligner nucmer included within it are among the most widely used alignment packages in genomics. Since the last major release of MUMmer version 3 in 2004, it has been applied to many types of problems including aligning whole genome sequences, aligning reads to a reference genome, and comparing different assemblies of the same genome. Despite its broad utility, MUMmer3 has limitations that can make it difficult to use for large genomes and for the very large sequence data sets that are common today. In this paper we describe MUMmer4, a substantially improved version of MUMmer that addresses genome size constraints by changing the 32-bit suffix tree data structure at the core of MUMmer to a 48-bit suffix array, and that offers improved speed through parallel processing of input query sequences. With a theoretical limit on the input size of 141Tbp, MUMmer4 can now work with input sequences of any biologically realistic length. We show that as a result of these enhancements, the nucmer program in MUMmer4 is easily able to handle alignments of large genomes; we illustrate this with an alignment of the human and chimpanzee genomes, which allows us to compute that the two species are 98% identical across 96% of their length. With the enhancements described here, MUMmer4 can also be used to efficiently align reads to reference genomes, although it is less sensitive and accurate than the dedicated read aligners. The nucmer aligner in MUMmer4 can now be called from scripting languages such as Perl, Python and Ruby. These improvements make MUMer4 one the most versatile genome alignment packages available.

Abstract: A new algorithm is presented for constructing auxiliary digital search trees to aid in exact-match substring searching. This algorithm has the same asymptotic running time bound as previously published algorithms, but is more economical in space. Some implementation considerations are discussed, and new work on the modification of these search trees in response to incremental changes in the strings they index (the update problem) is presented.

Abstract: An on-line algorithm is presented for constructing the suffix tree for a given string in time linear in the length of the string. The new algorithm has the desirable property of processing the string symbol by symbol from left to right. It always has the suffix tree for the scanned part of the string ready. The method is developed as a linear-time version of a very simple algorithm for (quadratic size) suffixtries. Regardless of its quadratic worst case this latter algorithm can be a good practical method when the string is not too long. Another variation of this method is shown to give, in a natural way, the well-known algorithms for constructing suffix automata (DAWGs).