Sorting suffixes of two-pattern strings
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...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Conference Paper |
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Vydavatelstvi CVUT
2004
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| Online Access: | http://hdl.handle.net/20.500.11937/16490 |
| _version_ | 1848749191499612160 |
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| author | Franek, F. Smyth, Bill |
| author2 | Milan Simanek |
| author_facet | Milan Simanek Franek, F. Smyth, Bill |
| author_sort | Franek, F. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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 analgorithm 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. |
| first_indexed | 2025-11-14T07:17:01Z |
| format | Conference Paper |
| id | curtin-20.500.11937-16490 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:17:01Z |
| publishDate | 2004 |
| publisher | Vydavatelstvi CVUT |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-164902022-10-06T07:15:58Z Sorting suffixes of two-pattern strings Franek, F. Smyth, Bill Milan Simanek Jan Holub 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 analgorithm 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. 2004 Conference Paper http://hdl.handle.net/20.500.11937/16490 Vydavatelstvi CVUT fulltext |
| spellingShingle | Franek, F. Smyth, Bill Sorting suffixes of two-pattern strings |
| title | Sorting suffixes of two-pattern strings |
| title_full | Sorting suffixes of two-pattern strings |
| title_fullStr | Sorting suffixes of two-pattern strings |
| title_full_unstemmed | Sorting suffixes of two-pattern strings |
| title_short | Sorting suffixes of two-pattern strings |
| title_sort | sorting suffixes of two-pattern strings |
| url | http://hdl.handle.net/20.500.11937/16490 |