Minimum Common String Partition Parameterized by Partition Size Is Fixed-Parameter Tractable

Bulteau, Laurent; Komusiewicz, Christian

doi:10.1137/1.9781611973402.8

Cited by 16 publications

(10 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…). Similarly, the sequence d A(5,7) of consecutive duos is mapped into the sequence d B (3,5) of consecutive duos; hence duos (A [5], A [6]), (A [6], A [7]) of A are preserved. The number of preserved duos induced by the mapping is 3.…”

Section: Preliminariesmentioning

confidence: 99%

Parameterized tractability of the maximum-duo preservation string mapping problem

Beretta

Castelli

Dondi

2016

Theoretical Computer Science

View full text Add to dashboard Cite

In this paper we investigate the parameterized complexity of the Maximum-Duo Preservation String Mapping Problem, the complementary of the Minimum Common String Partition Problem. We show that this problem is fixed-parameter tractable when parameterized by the number k of conserved duos, by first giving a parameterized algorithm based on the color-coding technique and then presenting a reduction to a kernel of size O(k 6 ).

show abstract

Section: Preliminariesmentioning

confidence: 99%

Parameterized tractability of the maximum-duo preservation string mapping problem

Beretta

Castelli

Dondi

2016

Theoretical Computer Science

View full text Add to dashboard Cite

show abstract

“…Note that MCSP has been proved to be in FPT with respect to the size of the solution [18]. It can be seen that this result can be adapted for the SMCR problem in the case = 1.…”

Section: Duomentioning

confidence: 76%

Sorting by Multi-Cut Rearrangements

et al. 2021

Self Cite

View full text Add to dashboard Cite

A multi-cut rearrangement of a string S is a string S′ obtained from S by an operation called k-cut rearrangement, that consists of (1) cutting S at a given number k of places in S, making S the concatenated string X1·X2·X3·…·Xk·Xk+1, where X1 and Xk+1 are possibly empty, and (2) rearranging the Xis so as to obtain S′=Xπ(1)·Xπ(2)·Xπ(3)·…·Xπ(k+1), π being a permutation on 1,2,…,k+1 satisfying π(1)=1 and π(k+1)=k+1. Given two strings S and T built on the same multiset of characters from an alphabet Σ, the Sorting by Multi-Cut Rearrangements (SMCR) problem asks whether a given number ℓ of k-cut rearrangements suffices to transform S into T. The SMCR problem generalizes several classical genomic rearrangements problems, such as Sorting by Transpositions and Sorting by Block Interchanges. It may also model chromoanagenesis, a recently discovered phenomenon consisting of massive simultaneous rearrangements. In this paper, we study the SMCR problem from an algorithmic complexity viewpoint. More precisely, we investigate its classical and parameterized complexity, as well as its approximability, in the general case or when S and T are permutations.

show abstract

“…Damaschke [15] presented the first fixedparameter algorithms for MCSP, for combined parameters such as "partition size plus repetition number of the input strings". 2 Subsequently, MCSP was shown to be fixedparameter tractable with the single parameter partition size [9]. Jiang et al [23] considered the combined parameter "partition size plus maximum occurrence d of any character" and showed that MCSP can be solved in time (d!)…”

Section: :2 Parameterized Complexity Of Maximum-duo Preservation String Mappingmentioning

confidence: 99%

Revisiting the parameterized complexity of Maximum-Duo Preservation String Mapping

Komusiewicz

Oliveira

Zehavi

2020

Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

In the Maximum-Duo Preservation String Mapping (Max-Duo PSM) problem, the input consists of two related strings A and B of length n and a nonnegative integer k. The objective is to determine whether there exists a mapping m from the set of positions of A to the set of positions of B that maps only to positions with the same character and preserves at least k duos, which are pairs of adjacent positions. We develop a randomized algorithm that solves Max-Duo PSM in time 4 k • n O(1) , and a deterministic algorithm that solves this problem in time 6.855 k • n O(1) . The previous best known (deterministic) algorithm for this problem has running time (8e) 2k+o(k) • n O(1) [Beretta et al., Theor. Comput. Sci. 2016]. We also show that Max-Duo PSM admits a problem kernel of size O(k 3 ), improving upon the previous best known problem kernel of size O(k 6 ).

show abstract

Minimum Common String Partition Parameterized by Partition Size Is Fixed-Parameter Tractable

Cited by 16 publications

References 20 publications

Parameterized tractability of the maximum-duo preservation string mapping problem

Parameterized tractability of the maximum-duo preservation string mapping problem

Sorting by Multi-Cut Rearrangements

Revisiting the parameterized complexity of Maximum-Duo Preservation String Mapping

Contact Info

Product

Resources

About