Randomized algorithms
On the Approximation of Shortest Common Supersequencesand Longest Common Subsequences
SIAM Journal on Computing
Upper bounds for the expected length of a longest common subsequence of two binary sequences
Random Structures & Algorithms
Algorithms for the Longest Common Subsequence Problem
Journal of the ACM (JACM)
Numerical computing with IEEE floating point arithmetic
Numerical computing with IEEE floating point arithmetic
MFCS '94 Proceedings of the 19th International Symposium on Mathematical Foundations of Computer Science 1994
Java(TM) Language Specification, The (3rd Edition) (Java (Addison-Wesley))
Java(TM) Language Specification, The (3rd Edition) (Java (Addison-Wesley))
On a speculated relation between chvátal–sankoff constants of several sequences
Combinatorics, Probability and Computing
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It has long been known [Chvátal and Sankoff 1975] that the average length of the longest common subsequence of two random strings of length n over an alphabet of size k is asymptotic to γkn for some constant γk depending on k. The value of these constants remains unknown, and a number of papers have proved upper and lower bounds on them. We discuss techniques, involving numerical calculations with recurrences on many variables, for determining lower and upper bounds on these constants. To our knowledge, the previous best-known lower and upper bounds for γ2 were those of Dančík and Paterson, approximately 0.773911 and 0.837623 [Dančík 1994; Dančík and Paterson 1995]. We improve these to 0.788071 and 0.826280. This upper bound is less than the γ2 given by Steele's old conjecture (see Steele [1997, page 3]) that γ2 = 2/(1 + &sqrt;2)≈ 0.828427. (As Steele points out, experimental evidence had already suggested that this conjectured value was too high.) Finally, we show that the upper bound technique described here could be used to produce, for any k, a sequence of upper bounds converging to γk, though the computation time grows very quickly as better bounds are guaranteed.