Parameterized tractability of the maximum-duo preservation string mapping problem

Beretta, Stefano; Castelli, Mauro; Dondi, Riccardo

doi:10.1016/j.tcs.2016.07.011

Cited by 7 publications

(24 citation statements)

References 22 publications

(50 reference statements)

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“…For the MDSM problem, we observe that since the MCSP problem is NP-hard [14], the MDSM problem (i.e., its maximization version) is also NP-hard, and in fact even APX-hard [4]. Moreover, the problem is also shown to be fixed-parameter tractable with respect to the number of duos preserved [2]. Boria et al [4] gave a 4-approximation algorithm for the MDSM problem, which was subsequently improved to algorithms with approximation factors of 7/2 [3], 3.25 [5] and (recently) (2 + ) for any > 0 [13].…”

Section: Introductionmentioning

confidence: 93%

Approximating Weighted Duo-Preservation in Comparative Genomics

Mehrabi

2017

Lecture Notes in Computer Science

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Motivated by comparative genomics, Chen et al. [9] introduced the Maximum Duo-preservation String Mapping (MDSM) problem in which we are given two strings s 1 and s 2 from the same alphabet and the goal is to find a mapping π between them so as to maximize the number of duos preserved. A duo is any two consecutive characters in a string and it is preserved in the mapping if its two consecutive characters in s 1 are mapped to same two consecutive characters in s 2 . The MDSM problem is known to be NP-hard and there are approximation algorithms for this problem [3,5,13], but all of them consider only the "unweighted" version of the problem in the sense that a duo from s 1 is preserved by mapping to any same duo in s 2 regardless of their positions in the respective strings. However, it is well-desired in comparative genomics to find mappings that consider preserving duos that are "closer" to each other under some distance measure [19].In this paper, we introduce a generalized version of the problem, called the Maximum-Weight Duo-preservation String Mapping (MWDSM) problem that captures both duos-preservation and duos-distance measures in the sense that mapping a duo from s 1 to each preserved duo in s 2 has a weight, indicating the "closeness" of the two duos. The objective of the MWDSM problem is to find a mapping so as to maximize the total weight of preserved duos. In this paper, we give a polynomial-time 6-approximation algorithm for this problem.

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Section: Introductionmentioning

confidence: 93%

Approximating Weighted Duo-Preservation in Comparative Genomics

Mehrabi

2017

Lecture Notes in Computer Science

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“…2. An FPT Algorithm for Max-Duo PSM Here, we briefly discuss the FPT algorithm for Max-Duo PSM we presented in [1] and why it is not correct.…”

Section: Maximum-duo Preservation String Mapping Problem (Max-duo Psm)mentioning

confidence: 99%

“…Let C = {c 1 , c 2 } be a set of colors and assume that the coloring assigns to positions 1, 3 and 4 color c 1 , and to position 2 color c 2 . The dynamic programming we presented in [1], allows us to map duo Next, we show how to correct the FPT algorithm. The main idea is to assign two distinct colors to positions j and j + 1 when (B[j], B[j + 1]) is preserved, thus applying the coloring to positions that generate a duo, instead of positions that induce a duo.…”

Section: Maximum-duo Preservation String Mapping Problem (Max-duo Psm)mentioning

confidence: 99%

“…In [1], we proved that the Maximum-Duo Preservation String Mapping Problem is FPT, and, in particular, we presented a FPT algorithm based on the color-coding technique. However, as we will show later in this paper, the algorithm is incorrect.…”

Section: Introductionmentioning

confidence: 99%

“…First, we present the definitions that will be useful for the FPT algorithm that we will describe in Section 2. Most of the definitions are as in [1], we include them for completeness.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Corrigendum to “Parameterized tractability of the maximum-duo preservation string mapping problem” [Theoret. Comput. Sci. 646 (2016) 16–25]

Beretta

Castelli

Dondi

2016

Theoretical Computer Science

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A $$(1.4 + \epsilon )$$-approximation algorithm for the 2-Max-Duo problem

et al. 2020

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The maximum duo-preservation string mapping (Max-Duo) problem is the complement of the well studied minimum common string partition (MCSP) problem, both of which have applications in many fields including text compression and bioinformatics. k-Max-Duo is the restricted version of Max-Duo, where every letter of the alphabet occurs at most k times in each of the strings, which is readily reduced into the well known maximum independent set (MIS) problem on a graph of maximum degree ∆ ≤ 6(k − 1). In particular, 2-Max-Duo can then be approximated arbitrarily close to 1.8 using the state-of-the-art approximation algorithm for the MIS problem. 2-Max-Duo was proved APX-hard and very recently a (1.6 +)-approximation was claimed, for any > 0. In this paper, we present a vertex-degree reduction technique, based on which, we show that 2-Max-Duo can be approximated arbitrarily close to 1.4.

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Parameterized tractability of the maximum-duo preservation string mapping problem

Cited by 7 publications

References 22 publications

Approximating Weighted Duo-Preservation in Comparative Genomics

Approximating Weighted Duo-Preservation in Comparative Genomics

Corrigendum to “Parameterized tractability of the maximum-duo preservation string mapping problem” [Theoret. Comput. Sci. 646 (2016) 16–25]

A $$(1.4 + \epsilon )$$-approximation algorithm for the 2-Max-Duo problem

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