Frantisek Franek and William F. Smyth

**Sorting suffixes of two-pattern strings**

Abstract: |

Recently, several authors presented linear recursive algorithms for
sorting suffixes of a string. All these algorithms employ a similar
three-step approach, based on an initial division of the suffixes
of x into two sets: in step 1
sort the first set using recursive reduction of the problem,
in step 2 determine the order of the suffixes in the second set based on
the order of the suffixes in the first set, and in step 3 merge the
two sets together.
To optimize such an algorithm either for space or time,
it may not be sufficient to optimize one of the three steps,
since in doing so, one might increase the resources required
for the others to an unacceptable extent.
Franek, Lu, and Smyth introduced two-pattern strings as a generalization of Sturmian strings. Like Sturmian strings, two-pattern strings are generated by iterated morphisms, but they exhibit a much richer structure. In this paper we show that the suffixes of two-pattern strings can be sorted in linear time using a variant of the three step approach outlined above. It turns out that, given the order of the suffixes in a two-pattern string, one can almost directly list in linear time all the suffixes of its expansion under a two-pattern morphism. |

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