Bounding the Expected Length of Longest Common Subsequences and Forests

1999 ◽  
Vol 32 (4) ◽  
pp. 435-452 ◽  
Author(s):  
R. A. Baeza-Yates ◽  
R. Gavaldà, G. Navarro ◽  
R. Scheihing
Keyword(s):  
Longest Common Subsequences ◽  
Expected Length

Longest common subsequences of two random sequences

1975 ◽  
Vol 12 (02) ◽  
pp. 306-315 ◽  
Author(s):  
Vacláv Chvátal ◽  
David Sankoff
Keyword(s):  
Monte Carlo ◽  
Molecular Evolution ◽  
Lower Bounds ◽  
Monte Carlo Methods ◽  
Longest Common Subsequence ◽  
Upper And Lower Bounds ◽  
Longest Common Subsequences ◽  
Expected Length ◽  
Common Subsequence ◽  
Limiting Behaviour

Summary Given two random k-ary sequences of length n, what is f(n,k), the expected length of their longest common subsequence? This problem arises in the study of molecular evolution. We calculate f(n,k) for all k, where n ≦ 5, and f(n,2) where n ≦ 10. We study the limiting behaviour of n –1 f(n,k) and derive upper and lower bounds on these limits for all k. Finally we estimate by Monte-Carlo methods f(100,k), f(1000,2) and f(5000,2).

Longest common subsequences of two random sequences

1975 ◽  
Vol 12 (2) ◽  
pp. 306-315 ◽  
Author(s):  
Vacláv Chvátal ◽  
David Sankoff
Keyword(s):  
Monte Carlo ◽  
Molecular Evolution ◽  
Lower Bounds ◽  
Monte Carlo Methods ◽  
Longest Common Subsequence ◽  
Upper And Lower Bounds ◽  
Longest Common Subsequences ◽  
Expected Length ◽  
Common Subsequence ◽  
Limiting Behaviour

SummaryGiven two random k-ary sequences of length n, what is f(n,k), the expected length of their longest common subsequence? This problem arises in the study of molecular evolution. We calculate f(n,k) for all k, where n ≦ 5, and f(n,2) where n ≦ 10. We study the limiting behaviour of n–1f(n,k) and derive upper and lower bounds on these limits for all k. Finally we estimate by Monte-Carlo methods f(100,k), f(1000,2) and f(5000,2).

scholarly journals A Note on the Expected Length of the Longest Common Subsequences of two i.i.d. Random Permutations

10.37236/6974 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Christian Houdré ◽  
Chen Xu
Keyword(s):  
Lower Bound ◽  
Random Permutations ◽  
Longest Common Subsequences ◽  
Expected Length ◽  
Uniform Case

We address a question and a conjecture on the expected length of the longest common subsequences of two i.i.d. random permutations of $[n]:=\{1,2,...,n\}$. The question is resolved by showing that the minimal expectation is not attained in the uniform case. The conjecture asserts that $\sqrt{n}$ is a lower bound on this expectation, but we only obtain $\sqrt[3]{n}$ for it.

Development and Application of a New PCR Method for Detection of Blumeria graminis f. sp. tritici

2018 ◽  
Vol 28 (3) ◽  
pp. 137-146 ◽  
Author(s):  
Adam Kuzdraliński ◽  
Hubert Szczerba ◽  
Anna Kot ◽  
Agnieszka Ostrowska ◽  
Michał Nowak ◽  
...  
Keyword(s):  
Dna Sequences ◽  
Puccinia Triticina ◽  
Blumeria Graminis ◽  
Pyrenophora Tritici Repentis ◽  
Field Samples ◽  
Expected Length ◽  
Pcr Assays ◽  
Primer Sets ◽  
Wheat Leaves ◽  
Species Specific

We developed new PCR assays that target beta-tubulin (<i>TUB2</i>) and 14 alpha-demethylase (<i>CYP51</i>) genes and used them for the species-specific detection of <i>Blumeria graminis</i> f. sp. <i>tritici</i> (<i>Bgt</i>). Based on fungi DNA sequences available in the NCBI (National Center for Biotechnology Information) GenBank database we developed simplex and duplex PCR assays. The specificities of the primer sets were evaluated using environmental samples of wheat leaves collected during the 2015/2016 growing season across Poland. Primer sets<i></i> LidBg17/18 and LidBg21/22 strongly amplified fragments of the expected length for all 67 tested samples. Primer specificity was confirmed using field samples of <i>Zymoseptoria tri­tici</i>, <i>Puccinia triticina</i> (syn.<i> P. recondita</i> f. sp.<i> tritici</i>), <i>P. striiformis</i> f. sp.<i> tritici</i>, and <i>Pyrenophora tritici-repentis</i>.

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