Sorting by Transpositions Is Difficult

Bulteau, Laurent; Fertin, Guillaume; Rusu, Irena

doi:10.1007/978-3-642-22006-7_55

Cited by 15 publications

(4 citation statements)

References 21 publications

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“…Recently, Bulteau et al 1 published a NP-hardness proof for this problem. Many algorithms were developed in order to¯nd a result close to the transposition distance, and most of them focused on improving the approximation factor or presenting novel data structures to the problem.…”

Section: Introductionmentioning

confidence: 98%

Heuristics for the Transposition Distance Problem

Dias

2013

J. Bioinform. Comput. Biol.

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Transpositions are large-scale mutational events that occur when a block of genes moves from a region of a chromosome to another region within the same chromosome. The transposition distance problem is the minimum number of transpositions required to transform one genome into another. Recently, Bulteau et al. [Bulteau L, Fertin G, Rusu U, Automata, Languages and Programming, Vol. 6755 of Lecture Notes in Computer Science, pp. 654-665, Springer Berlin, Heidelberg, 2011] proved that finding the transposition distance is a NP-Hard problem. Some approximation algorithm for this problem have been presented to date [Bafna V, Pevzner PA, SIAM J Discr Math11(2):224-240, 1998; Elias I, Hartman T, IEEE/ACM Trans Comput Biol Bioinform3(4):369-379, 2006; Mira CVG, Dias Z, Santos HP, Pinto GA, Walter ME, Proc 3rd Brazilian Symp Bioinformatics (BSB'2008), pp. 115-126, Santo André, Brazil, 2008; Walter MEMT, Dias Z, Meidanis J, Proc String Processing and Information Retrieval (SPIRE'2000), pp. 199-208, Coruña, Spain, 2000]. Here we focus on developing heuristics to provide an improved approximated solution. Our approach outperforms other algorithms on small sized permutations. We also show that our algorithm keeps the good performance on longer permutations.

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Section: Introductionmentioning

confidence: 98%

Heuristics for the Transposition Distance Problem

Dias

2013

J. Bioinform. Comput. Biol.

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“…While the characterization does not lead to a new algorithm for computating rotation distance between two trees, we believe that it might be useful in proving NP-compeleteness of the problem, given that the problem of transforming a given permutation to identity permutation (this is called the sorting problem for permutations) with minimum number of transposition operations is known to be NP-complete [BFR11].…”

Section: Introductionmentioning

confidence: 99%

Rotation Distance for Rank Bounded Trees

Anoop

Sarma

2022

Lecture Notes in Computer Science

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Computing the rotation distance between two binary trees with n internal nodes efficiently (in poly(n) time) is a long standing open question in the study of height balancing in tree data structures. In this paper, we initiate the study of this problem bounding the rank of the trees given at the input (defined in [EH89] in the context of decision trees).We define the rank-bounded rotation distance between two given binary trees T 1 and T 2 (with n internal nodes) of rank at most r, denoted by d r (T 1 , T 2 ), as the length of the shortest sequence of rotations that transforms T 1 to T 2 with the restriction that the intermediate trees must be of rank at most r. We show that the rotation distance problem reduces in polynomial time to the rank bounded rotation distance problem. This motivates the study of the problem in the combinatorial and algorithmic frontiers. Observing that trees with rank 1 coincide exactly with skew trees (binary trees where every internal node has at least one leaf as a child), we show the following results in this frontier :• We present an O(n 2 ) time algorithm for computing d 1 (T 1 , T 2 ). That is, when the given trees are skew trees (we call this variant as skew rotation distance problem) -where the intermediate trees are restricted to be skew as well. In particular, our techniques imply that for any two skew trees d(T 1 , T 2 ) ≤ n 2 .* A preliminary version of the paper containing a subset of results appeared in the proceedings of the 28th International Computing and Combinatorics Conference (COCOON 2022).

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“…The problem of determining the transposition distance of permutations is NP -hard [3] and there are no tight bounds for the distance. We combine the reality and desire diagram [1] and the unitary toric classes to obtain tight bounds for the transposition distance of lonely permutations.…”

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Upper bounds and exact values on transposition distance of permutations

Cunha¹,

Kowada²

2010

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One of the main operations of genome rearrangement is the transposition (exchange of contiguous blocks). Recently, the problem of computing the minimum amount of operations of transpositions needed to transform one sequence into another (transposition distance) between two permutations was proved to be N P -hard [3]. The exact distance is known for few cases. We show how to sort lonely permutations of the family u n,3 applying n 2 + 1 transpositions. Thus, if 4 divides n + 1 then the transposition distance is d t (u n,3 ) = n 2 + 1, and if 4 does not divide n + 1, we have that n 2 ≤ d t (u n,3 ) ≤ n 2 + 1.

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Sorting by Transpositions Is Difficult

Cited by 15 publications

References 21 publications

Heuristics for the Transposition Distance Problem

Heuristics for the Transposition Distance Problem

Rotation Distance for Rank Bounded Trees

Upper bounds and exact values on transposition distance of permutations

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