Banishing bias from consensus sequences

Ben-Dor, Amir; Lancia, Giuseppe; Perone, Jean‐Marc; Ravi, R.

doi:10.1007/3-540-63220-4_63

Cited by 54 publications

(37 citation statements)

References 17 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%

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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“…. , s n } of strings, say, each of length m. The Closest String problem [1,2,4,5,11] asks for the smallest d and a string s of length m which is within Hamming distance d to each s i ∈ S. This problem comes from coding theory when we are looking for a code not too far away from a given set of codes [4]. The problem is NP-hard [4,11].…”

Section: Introductionmentioning

confidence: 99%

“…Let d(s, s ′ ) denote the Hamming distance between s and s ′ . |s| is the length of s. s[i] is the i-th character of s. Thus, s = s [1]s [2] . .…”

Section: Introductionmentioning

confidence: 99%

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Closest String and Substring Problems

Wang¹

2008

Encyclopedia of Algorithms

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The problem of finding a center string that is 'close' to every given string arises and has many applications in computational molecular biology and coding theory.This problem has two versions: the Closest String problem and the Closest Substring problem. Assume that we are given a set of strings S = {s 1 , s 2 , . . . , s n } of strings, say, each of length m. The Closest String problem [1,2,4,5,11] asks for the smallest d and a string s of length m which is within Hamming distance d to each s i ∈ S. This problem comes from coding theory when we are looking for a code not too far away from a given set of codes [4]. The problem is NP-hard [4,11]. Berman et al [2] give a polynomial time algorithm for constant d. For super-logarithmic d, Ben-Dor et al [1] give an efficient approximation algorithm using linear program relaxation technique. The best polynomial time approximation has ratio 4 3 for all d, given by [11] and [5]. The Closest Substring problem looks for a string t which is within Hamming distance d away from a substring of each s i . This problem only has a 2 − 2 2|Σ|+1 approximation algorithm previously [11] and is much more elusive than the Closest String problem, but it has many applications in finding conserved regions, genetic drug target identification, and genetic probes in molecular biology [8,9,10,16,17,19,20,21,22,23,11]. Whether there are efficient approximation algorithms for both problems are major open questions in this area.We present two polynomial time approxmation algorithms with approximation ratio 1 + ǫ for any small ǫ to settle both questions.

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Banishing bias from consensus sequences

Cited by 54 publications

References 17 publications

Consensus Optimizing Both Distance Sum and Radius

Consensus Optimizing Both Distance Sum and Radius

On the Hardness of Counting and Sampling Center Strings

Closest String and Substring Problems

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