Greedy colorings of words

In the Binary Paint Shop Problem proposed by Epping et al. (2004) [4] one has to find a 0/1-coloring of the letters of a word in which every letter from some alphabet appears twice, such that the two occurrences of each letter are colored differently and the total number of color changes is minimize...

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Published inDiscrete Applied Mathematics Vol. 160; no. 12; pp. 1872 - 1874
Main Authors Rautenbach, Dieter, Szigeti, Zoltán
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2012
Elsevier
Subjects
Alphabets
Binary paint shop problem
Color
Coloring
Computer Science
Evenly laminar hypergraph
Greedy algorithm
Greedy algorithms
Laminar
Mathematical analysis
Odd transversal
Operations Research
Optimization
Evenly laminar hypergraph
Greedy algorithm
Binary paint shop problem
Odd transversal
Online AccessGet full text
ISSN0166-218X
1872-6771
DOI10.1016/j.dam.2012.03.038

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Abstract In the Binary Paint Shop Problem proposed by Epping et al. (2004) [4] one has to find a 0/1-coloring of the letters of a word in which every letter from some alphabet appears twice, such that the two occurrences of each letter are colored differently and the total number of color changes is minimized. Meunier and Sebő (2009) [5] and Amini et al. (2010) [1] gave sufficient conditions for the optimality of a natural greedy algorithm for this problem. Our result is a best possible generalization of their results. We prove that the greedy algorithm optimally colors every suitable subword of a given instance word w if and only if w contains none of the three words (a,b,a,c,c,b), (a,d,d,b,c,c,a,b), and (a,d,d,c,b,c,a,b) as a subword. Furthermore, we relate this to the fact that every member of a family of hypergraphs associated with w is evenly laminar.
AbstractList In the Binary Paint Shop Problem proposed by Epping et al. one has to find a 0/1-coloring of the letters of a word in which every letter from some alphabet appears twice, such that the two occurrences of each letter are colored differently and the total number of color changes is minimized. Meunier and Sebő and Amini et al. gave sufficient conditions for the optimality of a natural greedy algorithm for this problem. Our result is a best possible generalization of their results. We prove that the greedy algorithm optimally colors every suitable subword of a given instance word w if and only if w contains none of the three words (a,b,a,c,c,b), (a,d,d,b,c,c,a,b), and (a,d,d,c,b,c,a,b) as a subword. Furthermore, we relate this to the fact that every member of a family of hypergraphs associated with w is evenly laminar.
In the Binary Paint Shop Problem proposed by Epping et al. (2004) [4] one has to find a 0/1-coloring of the letters of a word in which every letter from some alphabet appears twice, such that the two occurrences of each letter are colored differently and the total number of color changes is minimized. Meunier and Sebő (2009) [5] and Amini et al. (2010) [1] gave sufficient conditions for the optimality of a natural greedy algorithm for this problem. Our result is a best possible generalization of their results. We prove that the greedy algorithm optimally colors every suitable subword of a given instance word w if and only if w contains none of the three words (a,b,a,c,c,b), (a,d,d,b,c,c,a,b), and (a,d,d,c,b,c,a,b) as a subword. Furthermore, we relate this to the fact that every member of a family of hypergraphs associated with w is evenly laminar.
In the Binary Paint Shop Problem proposed by Epping et al. (2004) [4] one has to find a 0 / 1 -coloring of the letters of a word in which every letter from some alphabet appears twice, such that the two occurrences of each letter are colored differently and the total number of color changes is minimized. Meunier and SebA (2009) [5] and Amini et al. (2010) [1] gave sufficient conditions for the optimality of a natural greedy algorithm for this problem. Our result is a best possible generalization of their results. We prove that the greedy algorithm optimally colors every suitable subword of a given instance word w if and only if w contains none of the three words ( a , b , a , c , c , b ) , ( a , d , d , b , c , c , a , b ) , and ( a , d , d , c , b , c , a , b ) as a subword. Furthermore, we relate this to the fact that every member of a family of hypergraphs associated with w is evenly laminar.
Author Rautenbach, Dieter
Szigeti, Zoltán
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CitedBy_id crossref_primary_10_1016_j_laa_2019_06_001
crossref_primary_10_1016_j_laa_2016_12_038
crossref_primary_10_1016_j_dam_2020_05_028
Cites_doi 10.1016/j.dam.2005.05.033
10.1016/S0166-218X(03)00442-6
10.1016/j.dam.2008.06.017
10.1016/j.jda.2010.12.003
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Keywords Evenly laminar hypergraph
Greedy algorithm
Binary paint shop problem
Odd transversal
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Bonsma, Epping, Hochstättler (br000015) 2006; 154
Meunier, Sebő (br000025) 2009; 157
Epping, Hochstättler, Oertel (br000020) 2004; 136
Amini, Meunier, Michel, Mohajeri (br000005) 2010; 8
Amini (10.1016/j.dam.2012.03.038_br000005) 2010; 8
Andres (10.1016/j.dam.2012.03.038_br000010) 2011; 9
Bonsma (10.1016/j.dam.2012.03.038_br000015) 2006; 154
Epping (10.1016/j.dam.2012.03.038_br000020) 2004; 136
Meunier (10.1016/j.dam.2012.03.038_br000025) 2009; 157
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Snippet In the Binary Paint Shop Problem proposed by Epping et al. (2004) [4] one has to find a 0/1-coloring of the letters of a word in which every letter from some...
In the Binary Paint Shop Problem proposed by Epping et al. (2004) [4] one has to find a 0 / 1 -coloring of the letters of a word in which every letter from...
In the Binary Paint Shop Problem proposed by Epping et al. one has to find a 0/1-coloring of the letters of a word in which every letter from some alphabet...
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SubjectTerms Alphabets
Binary paint shop problem
Color
Coloring
Computer Science
Evenly laminar hypergraph
Greedy algorithm
Greedy algorithms
Laminar
Mathematical analysis
Odd transversal
Operations Research
Optimization
Title Greedy colorings of words
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