2005
DOI: 10.1016/j.aim.2004.10.012
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Cited by 66 publications
(64 citation statements)
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“…For equally long sequences (i = j = n), it has been proved that L n,n ≈ γ c n for n ≫ 1, where the averaging is performed over all realizations of the random sequences. The constant γ c is known as the Chvátal-Sankoff constant which, to date, remains undetermined though there exists several bounds [12,14,15], a conjecture due to Steele [13] that γ c = 2/(1 + √ c) and a recent proof [16] that γ c → 2/ √ c as c → ∞. Unfortunately, no exact results are available for the finite size corrections to the leading behavior of the average L n,n , for the variance, and also for the full probability distribution of L n,n .…”
mentioning
confidence: 99%
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“…For equally long sequences (i = j = n), it has been proved that L n,n ≈ γ c n for n ≫ 1, where the averaging is performed over all realizations of the random sequences. The constant γ c is known as the Chvátal-Sankoff constant which, to date, remains undetermined though there exists several bounds [12,14,15], a conjecture due to Steele [13] that γ c = 2/(1 + √ c) and a recent proof [16] that γ c → 2/ √ c as c → ∞. Unfortunately, no exact results are available for the finite size corrections to the leading behavior of the average L n,n , for the variance, and also for the full probability distribution of L n,n .…”
mentioning
confidence: 99%
“…(6)- (7) also hold for the LCS model. Note that only the leading behavior of the average L n,n was known before [16] in the c → ∞ limit of the original LCS model. For finite c, while the above mapping to the LIS problem still works, the corresponding permutations of the LIS problem are not generated with equal probability and hence one can no longer use the BDJ results.…”
mentioning
confidence: 99%
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“…Although we are interested in the behavior of f ,h when h, we first analyze the behavior for h larger than (in particular when h is substantially larger than 2 /γ), and then show how to use this to obtain bounds for h; a similar approach was used in [5]. For n of size up to roughly 2 /γ we use part (b) of Definition 3 to bound F (n, , h) by the number G(n, ) of string pairs of size n with an lcs length of at least .…”
Section: Proof Of Theorem 14mentioning
confidence: 99%
“…However, both the use of mathematical apparatus as in [2,3] and numerical modeling (usually with special algorithms) [4,5,6] succeeded to clarify situation only in special cases m = n or α = 2 (see [7]). …”
Section: Introductionmentioning
confidence: 99%