Fast linear-space computations of longest common subsequences

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“…After the longest common subsequence has been calculated, the character sequences not in the LCS are correlated and saved as dynamic device mappings. The time required to compute dynamic confusions can be improved by using a more efficient LCS algorithm such as [1] or [2]. Furthermore, confusions can be computed by other means entirely, such as [10].…”

Simple and fast linear space computation of longest common subsequences

“…This was first suggested by Hirschberg [6]. Efficiency was later gained by concentrating on the computation of dominant matches [3]. We note that the algorithm from [11] can be easily modified to work in the same style while maintaining its time bound.…”

“…In its ideal form, i.e., when problems are evenly split into subproblems, one can expect a doubling of the original running time. But in order to split the problem evenly some methods have to calculate the length of an LCS in a separate stage preceding the divide and conquer scheme [3,8]. So their performance can be expected to be three times that of the original algorithm.…”

“…We highlight general structural facts concerning this symmetry and use these facts to develop a general method which (1) eliminates the need for a separate stage to compute the length; (2) splits an LCS evenly; (3) supports a speed up of the computation in practice. Using this method we are able to reduce the theoretical overhead factor to 2 for a variety of algorithms based on the same paradigm (contours) to compute an LCS [6,3,11]. We will shortly review this paradigm in Section 2.…”

Cache-oblivious dynamic programming

“…The problem of finding the longest common subsequence (LCS) of two sequences has a classic dynamic programming solution [7] that runs in Θ(mn) time, uses Θ(mn) space and performs Θ mn B I/Os when working on two sequences of lengths m and n. Linear space implementations of this algorithm [13,18,2] also have I/O complexity Ω mn B . The LCS problem arises in a wide range of applications, and is especially prominent in computational biology in sequence alignment.…”