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A faster algorithm for computing a longest common increasing subsequence

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44744

Katriel,  Irit
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44874

Kutz,  Martin
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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MPI-I-2005-1-007.pdf
(Any fulltext), 238KB

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Citation

Katriel, I., & Kutz, M.(2005). A faster algorithm for computing a longest common increasing subsequence (MPI-I-2005-1-007). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-684F-8
Abstract
Let $A=\langle a_1,\dots,a_n\rangle$ and $B=\langle b_1,\dots,b_m \rangle$ be two sequences with $m \ge n$, whose elements are drawn from a totally ordered set. We present an algorithm that finds a longest common increasing subsequence of $A$ and $B$ in $O(m\log m+n\ell\log n)$ time and $O(m + n\ell)$ space, where $\ell$ is the length of the output. A previous algorithm by Yang et al. needs $\Theta(mn)$ time and space, so ours is faster for a wide range of values of $m,n$ and $\ell$.