k-Chordal Graphs: from Cops and Robber to Compact Routing via Treewidth
| hal.structure.identifier | Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE] | |
| hal.structure.identifier | Laboratoire Bordelais de Recherche en Informatique [LaBRI] | |
| dc.contributor.author | KOSOWSKI, Adrian | |
| hal.structure.identifier | Algorithms, simulation, combinatorics and optimization for telecommunications [MASCOTTE] | |
| dc.contributor.author | LI, Bi | |
| hal.structure.identifier | Algorithms, simulation, combinatorics and optimization for telecommunications [MASCOTTE] | |
| dc.contributor.author | NISSE, Nicolas | |
| hal.structure.identifier | Facultad de Ingeniería y Ciencias [Santiago] | |
| dc.contributor.author | SUCHAN, Karol | |
| dc.date.accessioned | 2024-04-15T09:45:45Z | |
| dc.date.available | 2024-04-15T09:45:45Z | |
| dc.date.issued | 2012-02 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/197947 | |
| dc.description | RAPPORT | |
| dc.description.abstractEn | {\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. | |
| dc.description.sponsorship | Algorithmes de graphes parametres et exacts - ANR-09-BLAN-0159 | |
| dc.language.iso | en | |
| dc.subject.en | Treewidth | |
| dc.subject.en | chordality | |
| dc.subject.en | hyperbolicity | |
| dc.subject.en | compact routing | |
| dc.subject.en | cops and robber games | |
| dc.title.en | k-Chordal Graphs: from Cops and Robber to Compact Routing via Treewidth | |
| dc.type | Rapport | |
| dc.subject.hal | Informatique [cs]/Algorithme et structure de données [cs.DS] | |
| dc.subject.hal | Informatique [cs]/Mathématique discrète [cs.DM] | |
| dc.description.sponsorshipEurope | Experimental UpdateLess Evolutive Routing | |
| bordeaux.hal.laboratories | Laboratoire Bordelais de Recherche en Informatique (LaBRI) - UMR 5800 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.type.institution | INRIA | |
| hal.identifier | hal-00671861 | |
| hal.version | 1 | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00671861v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2012-02&rft.au=KOSOWSKI,%20Adrian&LI,%20Bi&NISSE,%20Nicolas&SUCHAN,%20Karol&rft.genre=unknown |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||