On the Parameterized Complexity of Computing Balanced Partitions in Graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F15%3A00237632" target="_blank" >RIV/68407700:21240/15:00237632 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/article/10.1007%2Fs00224-014-9557-5" target="_blank" >http://link.springer.com/article/10.1007%2Fs00224-014-9557-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00224-014-9557-5" target="_blank" >10.1007/s00224-014-9557-5</a>

Result language
angličtina
Original language name
On the Parameterized Complexity of Computing Balanced Partitions in Graphs
Original language description
A balanced partition is a clustering of a graph into a given number of equal-sized parts. For instance, the textsc{Bisection} problem asks to remove at most $k$ edges in order to partition the vertices into two equal-sized parts. We prove that textsc{Bisection} is FPT for the distance to constant cliquewidth if we are given the deletion set. This implies FPT algorithms for some well-studied parameters such as cluster vertex deletion number and feedback vertex set. However, we show that textsc{Bisection}does not admit polynomial-size kernels for these parameters. For the textsc{Vertex Bisection} problem, vertices need to be removed in order to obtain two equal-sized parts. We show that this problem is FPT for the number of removed vertices $k$ if the solution cuts the graph into a constant number $c$ of connected components. The latter condition is unavoidable, since we also prove that textsc{Vertex Bisection} is W[1]-hard w.r.t.~$(k,c)$. Our algorithms for finding bisections can easil
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
—

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)