Distinguishing string selection problems

Lanctot, J. Kevin; Li, Ming; Ma, Bin; Wang, Shaojiu; Zhang, Louxin

doi:10.1016/s0890-5401(03)00057-9

Cited by 218 publications

(173 citation statements)

References 8 publications

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“…For general k, the problem of finding a string X such that max 1≤i≤k d(X, S i ) ≤ r is NP-hard even when characters in strings are drawn from the binary alphabet [4]. Thus, attention has been restricted to approximation solutions [2,5,6,[11][12][13][14] and fixed-parameter solutions [7,8,14,15].…”

Section: Problem 2 Bounded Consensusmentioning

confidence: 99%

Consensus Optimizing Both Distance Sum and Radius

Amir

Landau

et al. 2009

String Processing and Information Retrieval

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Abstract. The consensus string problem is finding a representative string (consensus) of a given set S of strings. In this paper we deal with the consensus string problems optimizing both distance sum and radius, where the distance sum is the sum of (Hamming) distances from the strings in S to the consensus and the radius is the longest (Hamming) distance from the strings in S to the consensus. Although there have been results considering either distance sum or radius, there have been no results considering both as far as we know. We present two algorithms to solve the consensus string problems optimizing both distance sum and radius for three strings. The first algorithm finds the optimal consensus string that minimizes both distance sum and radius, and the second algorithm finds the bounded consensus string such that, given constants s and r, the distance sum is at most s and the radius is at most r. Both algorithms take linear time.

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Section: Problem 2 Bounded Consensusmentioning

confidence: 99%

Consensus Optimizing Both Distance Sum and Radius

Amir

Landau

et al. 2009

String Processing and Information Retrieval

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“…Finding similar regions in multiple DNA, RNA, or protein sequences plays an important role in many applications, including universal PCR primer design [4], [16], [18], [26], genetic probe design [16], antisense drug design [16], [3], finding transcription factor binding sites in genomic data [27], determining an unbiased consensus of a protein family [1], and motif-recognition [16], [24], [25]. The CLOSEST STRING problem formalizes these tasks and can be defined as follows: given a set of n strings S of length over the alphabet Σ and parameter d, the aim is determine if there exists a string s that has Hamming distance at most d from each string in S. We refer to s as the center string and let d(x, y) be the Hamming distance between strings x and y.…”

Section: Introductionmentioning

confidence: 99%

“…The CLOSEST STRING was first introduced and studied in the context bioinformatics by Lanctot et al [16]. Frances and Litman et al [11] showed the problem to be NP-complete, even in the special case when the alphabet is binary, implying there is unlikely to be a polynomial-time algorithm for this problem unless P = NP.…”

Section: Introductionmentioning

confidence: 99%

“…Frances and Litman et al [11] showed the problem to be NP-complete, even in the special case when the alphabet is binary, implying there is unlikely to be a polynomial-time algorithm for this problem unless P = NP. Since its introduction, the investigation of efficient approximation algorithms and exact heuristics for the CLOSEST STRING problem has been thoroughly considered [9], [10], [12], [16], [17], [19], [20].…”

Section: Introductionmentioning

confidence: 99%

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On the Hardness of Counting and Sampling Center Strings

Boucher

Omar

2010

String Processing and Information Retrieval

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Abstract-Given a set S of n strings, each of length , and a non-negative value d, we define a center string as a string of length that has Hamming distance at most d from each string in S. The #CLOSEST STRING problem aims to determine the number of unique center strings for a given set of strings S and input parameters n, , and d. We show #CLOSEST STRING is impossible to solve exactly or even approximately in polynomial time, and that restricting #CLOSEST STRING so that any one of the parameters n, , or d is fixed leads to an FPRAS. We show equivalent results for the problem of efficiently sampling center strings uniformly at random.Index Terms-biological sequence analysis, motif recognition, fully polynomial-time randomized approximation scheme (FPRAS), fully polynomial almost uniform sampler (FPAUS), computational complexity.

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“…Lanctot et al [2] designed 4 3 approximation algorithms, Li et al [3] presented a PTAS. They used the standard linear programming and random rounding technique in their approximation algorithms.…”

Section: Introductionmentioning

confidence: 99%

Parallel Genetic Algorithm and Parallel Simulated Annealing Algorithm for the Closest String Problem

Sýkora

2005

Advanced Data Mining and Applications

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Distinguishing string selection problems

Cited by 218 publications

References 8 publications

Consensus Optimizing Both Distance Sum and Radius

Consensus Optimizing Both Distance Sum and Radius

On the Hardness of Counting and Sampling Center Strings

Parallel Genetic Algorithm and Parallel Simulated Annealing Algorithm for the Closest String Problem

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