Routage compact optimal dans les (k, r)-constellations

(Fraigniaud et al., 2001) and independently (Thorup et al., 2001) show that n-node trees support routing schemes with message headers, node addresses, and routing tables of O(log n) bits. It still open to known if this optimal result can be extended to the tree-width two graphs. The best known routing scheme require O(log n) bits (cf. (Peleg, 2000)). In this article, we extend this optimal result to (k, r)-constellations, i.e., K2,r-minor free networks whose bi-connected components are outerplanar by deleting k vertices. For example, (2, 4)constellations contain trees, outerplanars and more generally all K2,4-minor free networks. MOTS-CLÉS : routage compact, graphe sans mineur, graphe planaire, graphe planaire-extérieur.