Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

Maximum-Sum Segments

  • Kun-Mao Chao
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_226-2

Years and Authors of Summarized Original Work

2002; Lin, Jiang, Chao

Problem Definition

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

Keywords

Shortest path Longest path 
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Recommended Reading

  1. 1.
    Bae SE, Takaoka T (2004) Algorithms for the problem of k maximum sums and a VLSI algorithm for the k maximum subarrays problem. In: Proceedings of the 7th international symposium on parallel architectures, algorithms and networks, Hong Kong, pp 247–253Google Scholar
  2. 2.
    Bentley J (1986) Programming pearls. Addison-Wesley, ReadingGoogle 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 K-Y, Chao K-M (2004) On the range maximum-sum segment query problem. In: Proceedings of the 15th international symposium on algorithms and computation, Hong Kong. LNCS, vol 3341, pp 294–305Google Scholar
  6. 6.
    Chen K-Y, Chao K-M (2005) Optimal algorithms for locating the longest and shortest segments satisfying a sum or an average constraint. Inf Process Lett 96:197–201CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Cheng C-H, Chen K-Y, Tien W-C, Chao K-M (2006) Improved algorithms for the k maximum-sum problems. Theor Comput Sci 362:162–170CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Csűrös M (2004) Maximum-scoring segment sets. IEEE/ACM Trans Comput Biol Bioinform 1:139–150CrossRefGoogle Scholar
  9. 9.
    Eppstein D (1998) Finding the k shortest paths. SIAM J Comput 28:652–673CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Fan T-H, Lee S, Lu H-I, Tsou T-S, Wang T-C, Yao A (2003) An optimal algorithm for maximum-sum segment and its application in bioinformatics. In: Proceedings of the eighth international conference on implementation and application of automata, Santa Barbara. LNCS, vol 2759, pp 251–257Google Scholar
  11. 11.
    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
  12. 12.
    Huang X (1994) An algorithm for identifying regions of a DNA sequence that satisfy a content requirement. Comput Appl Biosci 10:219–225Google 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 (2008) Algorithms for finding the weight-constrained k longest paths in a tree and the length-constrained k maximum-sum segments of a sequence. Theor Comput Sci 407:349–358CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Ruzzo WL, Tompa M (1999) A linear time algorithm for finding all maximal scoring subsequences. In: Proceedings of the 7th international conference on intelligent systems for molecular biology, Heidelberg, pp 234–241Google 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. Nucleic Acids 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