On Sorting of Signed Permutations by Prefix and Suffix Reversals and Transpositions

Lintzmayer, Carla Négri; Dias, Zanoni

doi:10.1007/978-3-319-07953-0_12

Cited by 6 publications

(5 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Based on the algorithms that exist for the traditional problems of Sorting by Prefix Transpositions [20], Sorting by Prefix Reversals and Transpositions [21], Sorting by Prefix and Suffix Reversals, Sorting by Prefix and Suffix Transpositions, Sorting by Prefix and Suffix Reversals and Transpositions [23], and their signed variation [24], and based on the idea described for WUpRg, we can developed O (n)-approximation algorithms for all the other problems we are considering (called WUpTg, WUpRTg, WUpsRg, WUpsTg, WUpsRTg, WSpRg, WSpRTg, WSpsRg, and WSpsRTg, respectively). These algorithms are greedy in the sense of removal of breakpoints and of cost of the operation(s) performed, and that is why their names end with a "g".…”

Section: Build_permutation_ (N)mentioning

confidence: 99%

See 1 more Smart Citation

Approximation algorithms for sorting by length-weighted prefix and suffix operations

Lintzmayer

Fertin

Dias

2015

Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

International audienceThe traditional approach for the problems of sorting permutations by rearrangements is to consider that all operations have the same unitary cost. In this case, the goal is to find the minimum number of allowed rearrangements that are needed to sort a given permutation, and numerous efforts have been made over the past years regarding these problems. On the other hand, a long rearrangement (which is in fact a mutation) is more likely to disturb the organism. Therefore, weights based on the length of the segment involved may have an important role in the evolutionary process. In this paper we present the first results regarding problems of sorting permutations by length-weighted operations that consider rearrangement models with prefix and suffix variations of reversals and transpositions, which are the two most common types of genome rearrangements. Our main results are O(lg2⁡n)O(lg2⁡n)-approximation algorithms for 10 such problems

show abstract

Section: Build_permutation_ (N)mentioning

confidence: 99%

“…Lintzmayer and Dias [23][24][25] introduced new problems for which signed and unsigned suffix rearrangements are allowed along with their prefix versions, and presented approximation algorithms for them.…”

Section: Introductionmentioning

confidence: 99%

Approximation algorithms for sorting by length-weighted prefix and suffix operations

Lintzmayer

Fertin

Dias

2015

Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…. p j ) with j ≥ i between p 1 − 1 and its successor (whose positions are a − 1 and a; steps [11][12][13][14][15][16][17] or between p 1 + 1 and its successor (whose positions are b − 1 and b; steps 19-25). Such a move is performed only if it is possible to chose j such that, once the block (p 1 .…”

Section: Sorting By Prefix/suffix Transpositions and Reversals In O(n...mentioning

confidence: 99%

log-Lists and their applications to sorting by transpositions, reversals and block-interchanges

Rusu

2017

Theoretical Computer Science

View full text Add to dashboard Cite

Link-cut trees have been introduced by D.D. Sleator and R.E. Tarjan (Journal of Computer and System Sciences, 1983) with the aim of efficiently maintaining a forest of vertex-disjoint dynamic rooted trees under cut and link operations. These operations respectively disconnect a subtree from a tree, and join two trees by an edge. Additionally, link-cut trees allow to change the root of a tree and to perform a number of updates and queries on cost values defined on the arcs of the trees. All these operations are performed in O(log n) amortized or worst-case time, depending on the implementation, where n is the total size of the forest.In this paper, we show that a list of elements implemented using link-cut trees (we call it a log-list) allows us to obtain a common running time of O(log n) for the classical operations on lists, but also for some other essential operations that usually take linear time on lists. Such operations require to find the minimum/maximum element in a sublist defined by its endpoints, the position of a given element in the list or the element placed at a given position in the list; or they require to add a value a, or to multiply by −1, all the elements in a sublist.Furthermore, we use log-lists to implement several existing algorithms for sorting permutations by transpositions and/or reversals and/or block-interchanges, and obtain O(n log n) running time for all of them. In this way, the running time of several algorithms is improved, whereas in other cases our algorithms perform as well as the best existing implementations.

show abstract

“…In addition to these, recently, several studies involving variations of the transposition event and also rearrangement events that combine transposition with other events, e.g. reversals, have been proposed [6,19,20,26]. In 2012, Bulteau, Fertin and Rusu [2] demonstrated that TDP is N P-hard.…”

Section: Introductionmentioning

confidence: 99%

A new 1.375-approximation algorithm for Sorting By Transpositions

Silva¹,

Kowada²,

Rocco³

et al. 2020

Preprint

View full text Add to dashboard Cite

In genome rearrangements, the mutational event transposition swaps two adjacent blocks of genes in one chromosome. The Transposition Distance Problem (TDP) aims to find the minimum number of transpositions (distance) required to transform one chromosome into another, both represented as permutations. Setting the target permutation as the identity permutation, makes the TDP equivalent to the problem of Sorting by Transpositions (SBT).TDP is N P-hard and the best approximation algorithm with a 1.375 ratio was proposed in 2006 by Elias and Hartman. Their algorithm employs a technique called simplification to transform an input permutation π into a simple permutation π, obtained by inserting new symbols into π in a way that the lower bound of the transposition distance of π is kept on π. The assumption is that handling with simple permutations is easier than with normal ones. A sequence of transpositions sorting π can be mimicked to sort π.In this work, we first show that the algorithm of Elias and Hartman may require one transposition above the intended approximation ratio of 1.375, depending on how the input permutation is simplified. Then, we propose a new 1.375-approximation algorithm to solve TDP based on an algebraic formalism which does not use simplification, ensuring the approximation ratio of 1.375 for all the permutations in the Symmetric Group S n . We also propose a new upper bound for the transposition distance.Implementations of our algorithm and the one of Elias and Hartman were audited using GRAAu tool. The results show that, taking as input short permutations with maximum length 13, in addition to keeping the approximation below the 1.375 ratio, our algorithm returns a higher percentage of exact distances than the one of Elias and Hartman.

show abstract

On Sorting of Signed Permutations by Prefix and Suffix Reversals and Transpositions

Cited by 6 publications

References 12 publications

Approximation algorithms for sorting by length-weighted prefix and suffix operations

Approximation algorithms for sorting by length-weighted prefix and suffix operations

log-Lists and their applications to sorting by transpositions, reversals and block-interchanges

A new 1.375-approximation algorithm for Sorting By Transpositions

Contact Info

Product

Resources

About