HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation

A unified FPT Algorithm for Width of Partition Functions

Pascal Berthomé 1 Nicolas Nisse 2
2 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : During the last decades, several polynomial-time algorithms have been designed that decide if a graph has treewidth (resp., pathwidth, branchwidth, etc.) at most $k$, where $k$ is a fixed parameter. Amini {\it et al.} (to appear in SIAM J. Discrete Maths.) use the notions of partitioning-trees and partition functions as a generalized view of classical decompositions of graphs, namely tree-decomposition, path-decomposition, branch-decomposition, etc. In this paper, we propose a set of simple sufficient conditions on a partition function $\Phi$, that ensures the existence of a linear-time explicit algorithm deciding if a set $A$ has $\Phi$-width at most $k$ ($k$ fixed). In particular, the algorithm we propose unifies the existing algorithms for treewidth, pathwidth, linearwidth, branchwidth, carvingwidth and cutwidth. It also provides the first Fixed Parameter Tractable linear-time algorithm deciding if the $q$-branched treewidth, defined by Fomin {\it et al.} (Algorithmica 2007), of a graph is at most $k$ ($k$ and $q$ are fixed). Our decision algorithm can be turned into a constructive one by following the ideas of Bodlaender and Kloks (J. of Alg. 1996).
Complete list of metadata

Cited literature [19 references]  Display  Hide  Download

Contributor : Nicolas Nisse Connect in order to contact the contributor
Submitted on : Monday, September 15, 2008 - 6:39:29 PM
Last modification on : Friday, February 4, 2022 - 3:14:46 AM
Long-term archiving on: : Thursday, June 3, 2010 - 7:50:54 PM


Files produced by the author(s)


  • HAL Id : inria-00321766, version 1


Pascal Berthomé, Nicolas Nisse. A unified FPT Algorithm for Width of Partition Functions. [Research Report] RR-6646, INRIA. 2008, pp.36. ⟨inria-00321766⟩



Record views


Files downloads