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...ignment with maximal unique matches (MUMs), maximal matches, maximal repeats or exact matches, and then join these exact matches with gapped alignment. Similarly, Segemehl initiates the alignment with the longest prefix match of each suffix, but it may also enumerate mismatches and gaps at certain positions of the query to reduce false alignments. OASIS and BWT-SW essentially sample substrings of the reference by a top–down traversal on the trie and align these substrings against the query by dynamic programming. BWA-SW furthers BWT-SW by representing the query as a directed word graph (DAWG) [52], which also enables it to deploy heuristics to accelerate alignment. Bowtie and BWA also sample short substrings of the reference, but instead of performing dynamic programming, they compare the query and sampled substrings only allowing a few differences. In addition, as they require the entire read to be aligned, the traversal of the trie can be bounded since it is unnecessary to descend deeper in the trie if it can be predicted that doing so leads to an alignment with excessive mismatches and gaps. Alternatively, Bowtie and BWA can be considered to enumerate all combinations of possible mi...

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...nd efficient as suffix trees (and they are not expected to be). Second, the direct construction methods for these index structures do not run in linear worst case time. ¶ Directed acyclic word graphs =-=[12,13]-=- (dawgs, for short), and more space efficient variants thereof [14,15], have essentially the same applications as suffix trees. The compact dawg, which is the most space efficient of these index struc...

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...ates of the suffix automaton of a word of length n is less than 2n, and the number of its edges is less than 3n. Algorithms for constructing suffix automata in linear time have been given in [23] and =-=[17]-=-, see again [24] for details. 9.2 Nondeterministic automata A nondeterministic automaton is minimal if it has the minimal number of states among all automata recognizing the same language. Nondetermin...

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...14] using another method. Additional results needed by the application are given in Appendix A. Many results of Sections 4 to 6 have been independently discovered by Blumer et al. and may be found in =-=[6]-=-. This paper also contains an interesting discussion on different algorithms following Weiner's approach. 1. Factor automata All the words considered in this paper are elements of the free monoid A* g...

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...mma \Gamma \Gamma\Psi ceae a e a 1. ast(t) has O(n 2 ) nodes (take e.g. t = a n c n in Figure 4). However, isomorphic subtrees 2 can be shared [10]. Sharing brings the space requirements down to O(n) =-=[8, 12]-=-. However, subtree sharing may be impossible, when leaves are to be annotated with extra information. 2. cst(t) has O(n) nodes, as all inner nodes are branching, and there are at most n leaves. The ed...