Please cite this article in press as: M. Crochemore et al., Linear-size suffix tries, Theoret. Comput. Sci. (2016), http://dx.doi.org/10.1016/j.tcs. 2016.04.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Linear-Size Suffix TriesSuffix trees are highly regarded data structures for text indexing and string algorithms [MCreight 76, Weiner 73]. For any given string w of length n = |w|, a suffix tree for w takes O(n) nodes and links. It is often presented as a compacted version of a suffix trie for w, where the latter is the trie (or digital search tree) built on the suffixes of w. Here the compaction process replaces each maximal chain of unary nodes with a single arc. For this, the suffix tree requires that the labels of its arcs are substrings encoded as pointers to w (or equivalent information). On the contrary, the arcs of the suffix trie are labeled by single symbols but there can be Θ(n 2 ) nodes and links for suffix tries in the worst case because of their unary nodes. It is an interesting question if the suffix trie can be stored using O(n) nodes. We present the linear-size suffix trie, which guarantees O(n) nodes. We use a new technique for reducing the number of unary nodes to O(n), that stems from some results on antidictionaries. For instance, by using the linear-size suffix trie, we are able to check whether a pattern p of length m = |p| occurs in w in O(m log |Σ|) time and we can find the longest common substring of two strings w 1 and w 2 in O((|w 1 | + |w 2 |) log |Σ|) time for an alphabet Σ.

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In this paper we define Sturmian graphs and we prove that all of them have a certain "counting" property. We show deep connections between this counting property and two conjectures, by Moser and by Zaremba, on the continued fraction expansion of real numbers. These graphs turn out to be the underlying graphs of compact directed acyclic word graphs of central Sturmian words. In order to prove this result, we give a characterization of the maximal repeats of central Sturmian words. We show also that, in analogy with the case of Sturmian words, these graphs converge to infinite ones.

We describe a new technique for reducing the number of nodes and symbols in automata based on tries. The technique stems from some results on anti-dictionaries for data compression and does not need to retain the input string, differently from other methods based on compact automata. The net effect is that of obtaining a lighter automaton than the directed acyclic word graph (DAWG) of Blumer et al., as it uses less nodes, still with arcs labeled by single characters