max planck institut
informatik

# MPI-I-2005-1-007

## A faster algorithm for computing a longest common increasing subsequence

### Katriel, Irit and Kutz, Martin

MPI-I-2005-1-007. March 2005, 13 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
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 $\ell$.
Acknowledgement:
References to related material:

191 KBytes; 237 KBytes
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URL to this document: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/2005-1-007
BibTeX
@TECHREPORT{KatrielKutz2005,
AUTHOR = {Katriel, Irit and Kutz, Martin},
TITLE = {A faster algorithm for computing a longest common increasing
subsequence},
TYPE = {Research Report},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},
NUMBER = {MPI-I-2005-1-007},
MONTH = {March},
YEAR = {2005},
ISSN = {0946-011X},
}