Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

Maximum-Average Segments

  • Kun-Mao ChaoEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_224-2

Years and Authors of Summarized Original Work

1994; Huang

Problem Definition

Given a sequence of numbers, \(A =\langle a_{1},a_{2},\ldots ,a_{n}\rangle\)


Maximum-average segment 
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Recommended Reading

  1. 1.
    Arslan A, Eğecioğlu Ö, Pevzner P (2001) A new approach to sequence comparison: normalized sequence alignment. Bioinformatics 17:327–337CrossRefGoogle Scholar
  2. 2.
    Bergkvist A, Damaschke P (2005) Fast algorithms for finding disjoint subsequences with extremal densities. In: Proceedings of the 16th annual international symposium on algorithms and computation, Sanya. Lecture notes in computer science, vol 3827, pp 714–723Google Scholar
  3. 3.
    Burton BA (2011) Searching a bitstream in linear time for the longest substring of any given density. Algorithmica 61:555–579CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Burton BA, Hiron M (2013) Locating regions in a sequence under density constraints. SIAM J Comput 42:1201–1215CrossRefzbMATHGoogle Scholar
  5. 5.
    Chen YH, Lu HI, Tang CY (2005) Disjoint segments with maximum density. In: Proceedings of the 5th annual international conference on computational science, Atlanta, pp 845–850Google Scholar
  6. 6.
    Chung K-M, Lu H-I (2004) An optimal algorithm for the maximum-density segment problem. SIAM J Comput 34:373–387CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Fukuda T, Morimoto Y, Morishita S, Tokuyama T (1999) Mining optimized association rules for numeric attributes. J Comput Syst Sci 58:1–12CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Goldwasser MH, Kao M-Y, Lu H-I (2005) Linear-time algorithms for computing maximum-density sequence segments with bioinformatics applications. J Comput Syst Sci 70:128–144CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Hsieh Y-H, Yu C-C, Wang B-F (2008) Optimal algorithms for the interval location problem with range constraints on length and average. IEEE/ACM Trans Comput Biol Bioinform 5:281–290CrossRefGoogle Scholar
  10. 10.
    Huang X (1994) An algorithm for identifying regions of a DNA sequence that satisfy a content requirement. Comput Appl Biosci 10:219–225Google Scholar
  11. 11.
    Kim SK (2003) Linear-time algorithm for finding a maximum-density segment of a sequence. Inf Process Lett 86:339–342CrossRefzbMATHGoogle Scholar
  12. 12.
    Lin Y-L, Huang X, Jiang T, Chao K-M (2003) MAVG: locating non-overlapping maximum average segments in a given sequence. Bioinformatics 19:151–152CrossRefGoogle Scholar
  13. 13.
    Lin Y-L, Jiang T, Chao K-M (2002) Efficient algorithms for locating the length-constrained heaviest segments with applications to biomolecular sequence analysis. J Comput Syst Sci 65:570–586CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Liu H-F, Chao K-M (2006) On locating disjoint segments with maximum sum of densities. In: Proceedings of the 17th annual international symposium on algorithms and computation, Kolkata. Lecture notes in computer science, vol 4288, pp 300–307Google Scholar
  15. 15.
    Nekrutenko A, Li WH (2000) Assessment of compositional heterogeneity within and between eukaryotic genomes. Genome Res 10:1986–1995CrossRefGoogle Scholar
  16. 16.
    Stojanovic N, Dewar K (2005) Identifying multiple alignment regions satisfying simple formulas and patterns. Bioinformatics 20:2140–2142CrossRefGoogle Scholar
  17. 17.
    Stojanovic N, Florea L, Riemer C, Gumucio D, Slightom J, Goodman M, Miller W, Hardison R (1999) Comparison of five methods for finding conserved sequences in multiple alignments of gene regulatory regions. Nucl Acid Res 19:3899–3910CrossRefGoogle Scholar
  18. 18.
    Zhang Z, Berman P, Wiehe T, Miller W (1999) Post-processing long pairwise alignments. Bioinformatics 15:1012–1019CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Computer Science and Information Engineering, National Taiwan UniversityTaipeiTaiwan