Distance and Routing Labeling Schemes for Cube-Free Median Graphs

Victor Chepoi (1, 2) , Arnaud Labourel (1, 3) , Sébastien Ratel (1)

1 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
2 ACRO - Algorithmique, Combinatoire et Recherche Opérationnelle
3 DALGO - Algorithmique Distribuée

Distance labeling schemes are schemes that label the vertices of a graph with short labels in such a way that the distance between any two vertices uuu and vvv can be determined efficiently by merely inspecting the labels of uuu and vvv, without using any other information. Similarly, routing labeling schemes label the vertices of a graph in a such a way that given the labels of a source node and a destination node, it is possible to compute efficiently the port number of the edge from the source that heads in the direction of the destination. One of important problems is finding natural classes of graphs admitting distance and/or routing labeling schemes with labels of polylogarithmic size. In this paper, we show that the class of cube-free median graphs on nnn nodes enjoys distance and routing labeling schemes with labels of O(log3n)O(log3⁡n)O(\log^3 n) bits.

Domaines: Calcul parallèle, distribué et partagé [cs.DC]; Mathématique discrète [cs.DM]; Algorithme et structure de données [cs.DS]; Géométrie algorithmique [cs.CG]; Combinatoire [math.CO]; Géométrie métrique [math.MG]

Victor Chepoi, Arnaud Labourel, Sébastien Ratel. Distance and Routing Labeling Schemes for Cube-Free Median Graphs. Algorithmica, 2021, 83 (1), pp.252-296. ⟨10.1007/s00453-020-00756-w⟩. ⟨hal-03287556⟩