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**1 - 2**of**2**### On-line Construction of compact suffix vectors and maximal repeats ∗

"... A suffix vector of a string is an index data structure equivalent to a suffix tree. It was first introduced by Monostori et al. in 2001 [9, 10, 11]. They proposed a linear construction algorithm of an extended suffix vector then another linear algorithm to transform an extended suffix vector into a ..."

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A suffix vector of a string is an index data structure equivalent to a suffix tree. It was first introduced by Monostori et al. in 2001 [9, 10, 11]. They proposed a linear construction algorithm of an extended suffix vector then another linear algorithm to transform an extended suffix vector into a more space economical compact suffix vector. We propose an on-line linear algorithm for directly constructing a compact suffix vector. Not only we show that it is possible to directly build a compact suffix vector but we will also show that this on-line construction can be faster than the construction of the extended suffix vector. Finally, we present an efficient method for computing maximal repeats using suffix vectors. 1

### On Sturmian Graphs?

"... 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 underl ..."

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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.