Sampling solution traces for the problem of sorting permutations by signed reversals
<p>Abstract</p> <p>Background</p> <p>Traditional algorithms to solve the problem of sorting by signed reversals output just one optimal solution while the space of all optimal solutions can be huge. A so-called trace represents a group of solutions which share the same...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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BMC
2012-06-01
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| Series: | Algorithms for Molecular Biology |
| Subjects: | |
| Online Access: | http://www.almob.org/content/7/1/18 |
| _version_ | 1811281257391194112 |
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| author | Baudet Christian Dias Zanoni Sagot Marie-France |
| author_facet | Baudet Christian Dias Zanoni Sagot Marie-France |
| author_sort | Baudet Christian |
| collection | DOAJ |
| description | <p>Abstract</p> <p>Background</p> <p>Traditional algorithms to solve the problem of sorting by signed reversals output just one optimal solution while the space of all optimal solutions can be huge. A so-called trace represents a group of solutions which share the same set of reversals that must be applied to sort the original permutation following a partial ordering. By using traces, we therefore can represent the set of optimal solutions in a more compact way. Algorithms for enumerating the complete set of traces of solutions were developed. However, due to their exponential complexity, their practical use is limited to small permutations. A partial enumeration of traces is a sampling of the complete set of traces and can be an alternative for the study of distinct evolutionary scenarios of big permutations. Ideally, the sampling should be done uniformly from the space of all optimal solutions. This is however conjectured to be <it>♯</it>P-complete.</p> <p>Results</p> <p>We propose and evaluate three algorithms for producing a sampling of the complete set of traces that instead can be shown in practice to preserve some of the characteristics of the space of all solutions. The first algorithm (<monospace>RA</monospace>) performs the construction of traces through a random selection of reversals on the list of optimal 1-sequences. The second algorithm (<monospace>DFALT</monospace>) consists in a slight modification of an algorithm that performs the complete enumeration of traces. Finally, the third algorithm (<monospace>SWA</monospace>) is based on a sliding window strategy to improve the enumeration of traces. All proposed algorithms were able to enumerate traces for permutations with up to 200 elements.</p> <p>Conclusions</p> <p>We analysed the distribution of the enumerated traces with respect to their height and average reversal length. Various works indicate that the reversal length can be an important aspect in genome rearrangements. The algorithms <monospace>RA</monospace> and <monospace>SWA</monospace> show a tendency to lose traces with high average reversal length. Such traces are however rare, and qualitatively our results show that, for testable-sized permutations, the algorithms <monospace>DFALT</monospace> and <monospace>SWA</monospace> produce distributions which approximate the reversal length distributions observed with a complete enumeration of the set of traces.</p> |
| first_indexed | 2024-04-13T01:29:15Z |
| format | Article |
| id | doaj.art-f433e9704e4248c1b77e18ba96dc5b85 |
| institution | Directory Open Access Journal |
| issn | 1748-7188 |
| language | English |
| last_indexed | 2024-04-13T01:29:15Z |
| publishDate | 2012-06-01 |
| publisher | BMC |
| record_format | Article |
| series | Algorithms for Molecular Biology |
| spelling | doaj.art-f433e9704e4248c1b77e18ba96dc5b852022-12-22T03:08:33ZengBMCAlgorithms for Molecular Biology1748-71882012-06-01711810.1186/1748-7188-7-18Sampling solution traces for the problem of sorting permutations by signed reversalsBaudet ChristianDias ZanoniSagot Marie-France<p>Abstract</p> <p>Background</p> <p>Traditional algorithms to solve the problem of sorting by signed reversals output just one optimal solution while the space of all optimal solutions can be huge. A so-called trace represents a group of solutions which share the same set of reversals that must be applied to sort the original permutation following a partial ordering. By using traces, we therefore can represent the set of optimal solutions in a more compact way. Algorithms for enumerating the complete set of traces of solutions were developed. However, due to their exponential complexity, their practical use is limited to small permutations. A partial enumeration of traces is a sampling of the complete set of traces and can be an alternative for the study of distinct evolutionary scenarios of big permutations. Ideally, the sampling should be done uniformly from the space of all optimal solutions. This is however conjectured to be <it>♯</it>P-complete.</p> <p>Results</p> <p>We propose and evaluate three algorithms for producing a sampling of the complete set of traces that instead can be shown in practice to preserve some of the characteristics of the space of all solutions. The first algorithm (<monospace>RA</monospace>) performs the construction of traces through a random selection of reversals on the list of optimal 1-sequences. The second algorithm (<monospace>DFALT</monospace>) consists in a slight modification of an algorithm that performs the complete enumeration of traces. Finally, the third algorithm (<monospace>SWA</monospace>) is based on a sliding window strategy to improve the enumeration of traces. All proposed algorithms were able to enumerate traces for permutations with up to 200 elements.</p> <p>Conclusions</p> <p>We analysed the distribution of the enumerated traces with respect to their height and average reversal length. Various works indicate that the reversal length can be an important aspect in genome rearrangements. The algorithms <monospace>RA</monospace> and <monospace>SWA</monospace> show a tendency to lose traces with high average reversal length. Such traces are however rare, and qualitatively our results show that, for testable-sized permutations, the algorithms <monospace>DFALT</monospace> and <monospace>SWA</monospace> produce distributions which approximate the reversal length distributions observed with a complete enumeration of the set of traces.</p>http://www.almob.org/content/7/1/18ReversalsTracesSamplingGenome rearrangement |
| spellingShingle | Baudet Christian Dias Zanoni Sagot Marie-France Sampling solution traces for the problem of sorting permutations by signed reversals Algorithms for Molecular Biology Reversals Traces Sampling Genome rearrangement |
| title | Sampling solution traces for the problem of sorting permutations by signed reversals |
| title_full | Sampling solution traces for the problem of sorting permutations by signed reversals |
| title_fullStr | Sampling solution traces for the problem of sorting permutations by signed reversals |
| title_full_unstemmed | Sampling solution traces for the problem of sorting permutations by signed reversals |
| title_short | Sampling solution traces for the problem of sorting permutations by signed reversals |
| title_sort | sampling solution traces for the problem of sorting permutations by signed reversals |
| topic | Reversals Traces Sampling Genome rearrangement |
| url | http://www.almob.org/content/7/1/18 |
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