KOSOWSKI, Adrian; LI, Bi; NISSE, Nicolas; SUCHAN, Karol

Métadonnées

Licence d’utilisation du document

KOSOWSKI, Adrian
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]

LI, Bi
Algorithms, simulation, combinatorics and optimization for telecommunications [MASCOTTE]

NISSE, Nicolas
Algorithms, simulation, combinatorics and optimization for telecommunications [MASCOTTE]

Langue

Rapport

Ce document a été publié dans

2012-02

Résumé en anglais

{\it Cops and robber games} concern a team of cops that must capture a robber moving in a graph. We consider the class of $k$-chordal graphs, i.e., graphs with no induced cycle of length greater than $k$, $k\geq 3$. We prove that $k-1$ cops are always sufficient to capture a robber in $k$-chordal graphs. This leads us to our main result, a new structural decomposition for a graph class including $k$-chordal graphs. We present a quadratic algorithm that, given a graph $G$ and $k\geq 3$, either returns an induced cycle larger than $k$ in $G$, or computes a {\it tree-decomposition} of $G$, each {\it bag} of which contains a dominating path with at most $k-1$ vertices. This allows us to prove that any $k$-chordal graph with maximum degree $\Delta$ has treewidth at most $(k-1)(\Delta-1)+2$, improving the $O(\Delta (\Delta-1)^{k-3})$ bound of Bodlaender and Thilikos (1997). Moreover, any graph admitting such a tree-decomposition has hyperbolicity $\leq\lfloor \frac{3}{2}k\rfloor$. As an application, for any $n$-node graph admitting such a tree-decomposition, we propose a {\it compact routing scheme} using routing tables, addresses and headers of size $O(\log n)$ bits and achieving an additive stretch of $O(k\log \Delta)$. As far as we know, this is the first routing scheme with $O(\log n)$-routing tables and small additive stretch for $k$-chordal graphs.< Réduire

Mots clés en anglais

Treewidth

chordality

hyperbolicity

compact routing

cops and robber games

URI

https://oskar-bordeaux.fr/handle/20.500.12278/197947

Projet Européen

Experimental UpdateLess Evolutive Routing

Project ANR

Algorithmes de graphes parametres et exacts - ANR-09-BLAN-0159

Origine

Importé de hal

Unités de recherche

Laboratoire Bordelais de Recherche en Informatique (LaBRI) - UMR 5800