The Inverse Voronoi Problem in Graphs I: Hardness

Edouard Bonnet (1) , Sergio Cabello (2) , Bojan Mohar (3) , Hubert Pérez-Rosés (4)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 FMF - Faculty of Mathematics and Physics [Ljubljana]
3 SFU.ca - Simon Fraser University = Université Simon Fraser
4 Universitat Rovira i Virgili

We introduce the inverse Voronoi diagram problem in graphs: given a graph G with positive edge-lengths and a collection of subsets of vertices of V (G), decide whether is a Voronoi diagram in G with respect to the shortest-path metric. We show that the problem is NP-hard, even for planar graphs where all the edges have unit length. We also study the parameterized complexity of the problem and show that the problem is W[1]-hard when parameterized by the number of Voronoi cells or by the pathwidth of the graph.

Mots clés: distances in graphs; Voronoi diagram; inverse Voronoi problem; NP-complete; parameterized complexity

Domaines: Informatique [cs]

Edouard Bonnet, Sergio Cabello, Bojan Mohar, Hubert Pérez-Rosés. The Inverse Voronoi Problem in Graphs I: Hardness. Algorithmica, 2020. ⟨hal-03015342⟩