# MPI-I-2003-1-010

## A linear time heuristic for the branch-decomposition of planar graphs

### Tamaki, Hisao

**MPI-I-2003-1-010**. March** **2003, 18 pages. | Status:** **available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:

Let $G$ be a biconnected planar graph given together with its planar drawing.

A {\em face-vertex walk} in $G$ of length $k$

is an alternating sequence $x_0, \ldots x_k$ of

vertices and faces (i.e., if $x_{i - 1}$ is a face then $x_i$ is

a vertex and vice versa) such that $x_{i - 1}$ and $x_i$ are incident

with each other for $1 \leq i \leq k$.

For each vertex or face $x$ of $G$, let $\alpha_x$ denote

the length of the shortest face-vertex walk from the outer face of $G$ to $x$.

Let $\alpha_G$ denote the maximum of $\alpha_x$ over all vertices/faces $x$.

We show that there always exits a branch-decomposition of $G$ with width

$\alpha_G$ and that such a decomposition

can be constructed in linear time. We also give experimental results,

in which we compare the width of our decomposition with the optimal

width and with the width obtained by some heuristics for general

graphs proposed by previous researchers, on test instances used

by those researchers.

On 56 out of the total 59 test instances, our

method gives a decomposition within additive 2 of the optimum width and

on 33 instances it achieves the optimum width.

Acknowledgement:** **

References to related material:

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**URL to this document: **http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/2003-1-010

**BibTeX**
`@TECHREPORT{``Tamaki2003``,`

` AUTHOR = {Tamaki, Hisao},`

` TITLE = {A linear time heuristic for the branch-decomposition of planar graphs},`

` TYPE = {Research Report},`

` INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},`

` ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},`

` NUMBER = {MPI-I-2003-1-010},`

` MONTH = {March},`

` YEAR = {2003},`

` ISSN = {0946-011X},`

`}`