scholarly journals Expected length of the longest common subsequence for large alphabets

2005 ◽  
Vol 197 (2) ◽  
pp. 480-498 ◽  
Author(s):  
Marcos Kiwi ◽  
Martin Loebl ◽  
Jiří Matoušek
Keyword(s):  
Longest Common Subsequence ◽  
Expected Length ◽  
Common Subsequence

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 On a Speculated Relation Between Chvátal–Sankoff Constants of Several Sequences

2009 ◽  
Vol 18 (4) ◽  
pp. 517-532
Author(s):  
M. KIWI ◽  
J. SOTO
Keyword(s):  
Lower Bounds ◽  
Longest Common Subsequence ◽  
Expected Length ◽  
Common Subsequence

It is well known that, when normalized byn, the expected length of a longest common subsequence ofdsequences of lengthnover an alphabet of size σ converges to a constant γσ,d. We disprove a speculation by Steele regarding a possible relation between γ2,dand γ2,2. In order to do that we also obtain some new lower bounds for γσ,d, when both σ anddare small integers.

Common Subsequences and Supersequences and their Expected Length

1998 ◽  
Vol 7 (4) ◽  
pp. 365-373 ◽  
Author(s):  
VLADO DANČÍK
Keyword(s):  
Longest Common Subsequence ◽  
Expected Length ◽  
Common Subsequence ◽  
Shortest Common Supersequence

Let f(n, k, l) be the expected length of a longest common subsequence of l sequences of length n over an alphabet of size k. It is known that there are constants γ(l)k such that f(n, k, l)→ γ(l)kn as n→∞, and we show that γ(l)k= Θ(k1/l−1) as k→∞. Bounds for the corresponding constants for the expected length of a shortest common supersequence are also presented.

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