Revisiting Radius, Diameter, and all Eccentricity Computation in Graphs through Certificates

Feodor F. Dragan (1) , Michel Habib (2, 3) , Laurent Viennot (2, 3)

1 Kent State University
2 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
3 GANG - Networks, Graphs and Algorithms

We introduce notions of certificates allowing to bound eccentricities in a graph. In particular , we revisit radius (minimum eccentricity) and diameter (maximum eccentricity) computation and explain the efficiency of practical radius and diameter algorithms by the existence of small certificates for radius and diameter plus few additional properties. We show how such computation is related to covering a graph with certain balls or complementary of balls. We introduce several new algorithmic techniques related to eccentricity computation and propose algorithms for radius, diameter and all eccentricities with theoretical guarantees with respect to certain graph parameters. This is complemented by experimental results on various real-world graphs showing that these parameters appear to be low in practice. We also obtain refined results in the case where the input graph has low doubling dimension, has low hyperbolicity, or is chordal.

Domaines: Réseaux et télécommunications [cs.NI]; Algorithme et structure de données [cs.DS]

Feodor F. Dragan, Michel Habib, Laurent Viennot. Revisiting Radius, Diameter, and all Eccentricity Computation in Graphs through Certificates. [Research Report] Inria Paris; Université paris diderot; Kent State University. 2018. ⟨hal-01729748⟩