# 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:

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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},`

`}`