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Article Dans Une Revue SIAM Journal on Computing Année : 2022

Diameter, eccentricities and distance oracle computations on H-minor free graphs and graphs of bounded (distance) VC-dimension

Résumé

Under the Strong Exponential-Time Hypothesis, the diameter of general unweighted graphs cannot be computed in truly subquadratic time (in the size n + m of the input), as shown by Roditty and Williams. Nevertheless there are several graph classes for which this can be done such as bounded-treewidth graphs, interval graphs and planar graphs, to name a few. We propose to study unweighted graphs of constant distance VC-dimension as a broad generalization of many such classes-where the distance VC-dimension of a graph G is defined as the VCdimension of its ball hypergraph: whose hyperedges are the balls of all possible radii and centers in G. In particular for any fixed H, the class of H-minor free graphs has distance VC-dimension at most |V (H)| − 1.
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Dates et versions

hal-03841015 , version 1 (06-11-2022)

Identifiants

Citer

Guillaume Ducoffe, Michel Habib, Laurent Viennot. Diameter, eccentricities and distance oracle computations on H-minor free graphs and graphs of bounded (distance) VC-dimension. SIAM Journal on Computing, 2022, 51 (5), pp.1506-1534. ⟨10.1137/20M136551X⟩. ⟨hal-03841015⟩
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