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A new practical linear space algorithm for the longest common subsequence problem

Heiko Goeman; Michael Clausen — 2002

Kybernetika

This paper deals with a new practical method for solving the longest common subsequence (LCS) problem. Given two strings of lengths $m$ and $n$ , $n \geq m$ , on an alphabet of size $s$ , we first present an algorithm which determines the length $p$ of an LCS in $O (n s + min {m p, p (n - p)})$ time and $O (n s)$ space. This result has been achieved before [ric94,ric95], but our algorithm is significantly faster than previous methods. We also provide a second algorithm which generates an LCS in $O (n s + min {m p, m log m + p (n - p)})$ time while preserving the linear space bound, thus solving...

Algebraic complexity theory. III: On the complexity of the computation of permanents. (Algebraische Komplexitätstheorie. III: Zur Berechnungskomplexität von Permanenten.)

Clausen, Michael — 1996

Séminaire Lotharingien de Combinatoire [electronic only]

Algebraic complexity theory. I: An introduction. (Algebraische Komplexitätstheorie. I: Eine Einführung.)

Bürgisser, Peter; Clausen, Michael — 1996

Séminaire Lotharingien de Combinatoire [electronic only]

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A new practical linear space algorithm for the longest common subsequence problem

Algebraic complexity theory. III: On the complexity of the computation of permanents. (Algebraische Komplexitätstheorie. III: Zur Berechnungskomplexität von Permanenten.)

Algebraic complexity theory. I: An introduction. (Algebraische Komplexitätstheorie. I: Eine Einführung.)