Efficient algorithms for consensus string problems minimizing both distance sum and radius

Amihood Amir; Gad M. Landau; Joong Chae Na; Heejin Park; Kunsoo Park; Jeong Seop Sim

doi:10.1016/j.tcs.2011.05.034

Efficient algorithms for consensus string problems minimizing both distance sum and radius

Amihood Amir, Gad M. Landau, Joong Chae Na, Heejin Park, Kunsoo Park, Jeong Seop Sim

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

The consensus (string) problem is finding a representative string, called a consensus, of a given set S of strings. In this paper we deal with consensus problems considering 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, to the best of our knowledge. We present the first algorithms for two consensus problems considering both distance sum and radius for three strings: one problem is to find an optimal consensus minimizing both distance sum and radius. The other problem is to find a bounded consensus such that the distance sum is at most s and the radius is at most r for given constants s and r. Our algorithms are based on characterization of the lower bounds of distance sum and radius, and thus they solve the problems efficiently. Both algorithms run in linear time.

Original language	English
Pages (from-to)	5239-5246
Number of pages	8
Journal	Theoretical Computer Science
Volume	412
Issue number	39
DOIs	https://doi.org/10.1016/j.tcs.2011.05.034
State	Published - 9 Sep 2011

Bibliographical note

Funding Information:
The first author was partially supported by NSF grant CCR-09-04581, ISF grant 347/09, the Israel–Korea Scientific Research Cooperation, and BSF grant 2008217. The second author was partially supported by the National Science Foundation Award 0904246, Israel Science Foundation grants 35/05 and 347/09, the Israel–Korea Scientific Research Cooperation, Yahoo, Grant No. 2008217 from the United States–Israel Binational Science Foundation (BSF) and DFG. The third author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0007860). The fourth author was partially supported by the Korea Foundation for International Cooperation of Science Technology (KICOS) through a grant provided by the Korean Ministry of Education, Science & Technology (MEST) in 2009 (No. K20717000007-09B0100-00710) and Frontier Functional Proteomics Project from Korean Ministry of Education, Science and Technology (FPR08-A1-020). The fifth author was supported by NAP of Korea Research Council of Fundamental Science & Technology. The sixth author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0090441) and by Inha University Research Grant.

Funding

The first author was partially supported by NSF grant CCR-09-04581, ISF grant 347/09, the Israel–Korea Scientific Research Cooperation, and BSF grant 2008217. The second author was partially supported by the National Science Foundation Award 0904246, Israel Science Foundation grants 35/05 and 347/09, the Israel–Korea Scientific Research Cooperation, Yahoo, Grant No. 2008217 from the United States–Israel Binational Science Foundation (BSF) and DFG. The third author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0007860). The fourth author was partially supported by the Korea Foundation for International Cooperation of Science Technology (KICOS) through a grant provided by the Korean Ministry of Education, Science & Technology (MEST) in 2009 (No. K20717000007-09B0100-00710) and Frontier Functional Proteomics Project from Korean Ministry of Education, Science and Technology (FPR08-A1-020). The fifth author was supported by NAP of Korea Research Council of Fundamental Science & Technology. The sixth author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0090441) and by Inha University Research Grant.

Funders	Funder number
Israel–Korea Scientific Research Cooperation
Korea Foundation for International Cooperation of Science Technology
National Science Foundation	CCR-09-04581, 0904246
Deutsche Forschungsgemeinschaft
United States-Israel Binational Science Foundation	2008217
Inha University
Korea Research Council of Fundamental Science and Technology	2009-0090441
National Research Foundation of Korea
Israel Science Foundation	35/05, 347/09
Ministry of Education, Science and Technology	K20717000007-09B0100-00710, FPR08-A1-020, 2011-0007860

Keywords

Consensus strings
Distance sum
Multiple alignments
Radius

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10.1016/j.tcs.2011.05.034

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title = "Efficient algorithms for consensus string problems minimizing both distance sum and radius",

abstract = "The consensus (string) problem is finding a representative string, called a consensus, of a given set S of strings. In this paper we deal with consensus problems considering 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, to the best of our knowledge. We present the first algorithms for two consensus problems considering both distance sum and radius for three strings: one problem is to find an optimal consensus minimizing both distance sum and radius. The other problem is to find a bounded consensus such that the distance sum is at most s and the radius is at most r for given constants s and r. Our algorithms are based on characterization of the lower bounds of distance sum and radius, and thus they solve the problems efficiently. Both algorithms run in linear time.",

keywords = "Consensus strings, Distance sum, Multiple alignments, Radius",

author = "Amihood Amir and Landau, {Gad M.} and Na, {Joong Chae} and Heejin Park and Kunsoo Park and Sim, {Jeong Seop}",

note = "Funding Information: The first author was partially supported by NSF grant CCR-09-04581, ISF grant 347/09, the Israel–Korea Scientific Research Cooperation, and BSF grant 2008217. The second author was partially supported by the National Science Foundation Award 0904246, Israel Science Foundation grants 35/05 and 347/09, the Israel–Korea Scientific Research Cooperation, Yahoo, Grant No. 2008217 from the United States–Israel Binational Science Foundation (BSF) and DFG. The third author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0007860). The fourth author was partially supported by the Korea Foundation for International Cooperation of Science Technology (KICOS) through a grant provided by the Korean Ministry of Education, Science & Technology (MEST) in 2009 (No. K20717000007-09B0100-00710) and Frontier Functional Proteomics Project from Korean Ministry of Education, Science and Technology (FPR08-A1-020). The fifth author was supported by NAP of Korea Research Council of Fundamental Science & Technology. The sixth author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0090441) and by Inha University Research Grant.",

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AU - Na, Joong Chae

AU - Park, Heejin

AU - Park, Kunsoo

AU - Sim, Jeong Seop

N1 - Funding Information: The first author was partially supported by NSF grant CCR-09-04581, ISF grant 347/09, the Israel–Korea Scientific Research Cooperation, and BSF grant 2008217. The second author was partially supported by the National Science Foundation Award 0904246, Israel Science Foundation grants 35/05 and 347/09, the Israel–Korea Scientific Research Cooperation, Yahoo, Grant No. 2008217 from the United States–Israel Binational Science Foundation (BSF) and DFG. The third author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0007860). The fourth author was partially supported by the Korea Foundation for International Cooperation of Science Technology (KICOS) through a grant provided by the Korean Ministry of Education, Science & Technology (MEST) in 2009 (No. K20717000007-09B0100-00710) and Frontier Functional Proteomics Project from Korean Ministry of Education, Science and Technology (FPR08-A1-020). The fifth author was supported by NAP of Korea Research Council of Fundamental Science & Technology. The sixth author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0090441) and by Inha University Research Grant.

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N2 - The consensus (string) problem is finding a representative string, called a consensus, of a given set S of strings. In this paper we deal with consensus problems considering 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, to the best of our knowledge. We present the first algorithms for two consensus problems considering both distance sum and radius for three strings: one problem is to find an optimal consensus minimizing both distance sum and radius. The other problem is to find a bounded consensus such that the distance sum is at most s and the radius is at most r for given constants s and r. Our algorithms are based on characterization of the lower bounds of distance sum and radius, and thus they solve the problems efficiently. Both algorithms run in linear time.

AB - The consensus (string) problem is finding a representative string, called a consensus, of a given set S of strings. In this paper we deal with consensus problems considering 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, to the best of our knowledge. We present the first algorithms for two consensus problems considering both distance sum and radius for three strings: one problem is to find an optimal consensus minimizing both distance sum and radius. The other problem is to find a bounded consensus such that the distance sum is at most s and the radius is at most r for given constants s and r. Our algorithms are based on characterization of the lower bounds of distance sum and radius, and thus they solve the problems efficiently. Both algorithms run in linear time.

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Efficient algorithms for consensus string problems minimizing both distance sum and radius

Abstract

Bibliographical note

Funding

Keywords

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