de.mpg.escidoc.pubman.appbase.FacesBean
English
 
Help Guide Disclaimer Contact us Login
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Report

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

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45588

Tamaki,  Hisao
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

Locator
There are no locators available
Fulltext (public)

2003-1-010
(Any fulltext), 11KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Tamaki, H.(2003). A linear time heuristic for the branch-decomposition of planar graphs (MPI-I-2003-1-010). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-6B37-6
Abstract
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.