The Inverse Voronoi Problem in Graphs I: Hardness

We introduce the inverse Voronoi diagram problem in graphs: given a graph G with positive edge-lengths and a collection U of subsets of vertices of V ( G ), decide whether U is a Voronoi diagram in G with respect to the shortest-path metric. We show that the problem is NP-hard, even for planar graph...

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Bibliographic Details
Published in:Algorithmica 2020-10, Vol.82 (10), p.3018-3040
Main Authors: Bonnet, Édouard, Cabello, Sergio, Mohar, Bojan, Pérez-Rosés, Hebert
Format: Article
Language:English
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Apexes
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Graph theory
Graphs
Mathematics of Computing
Parameterization
Shortest path planning
Theory of Computation
Voronoi graphs
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Summary:We introduce the inverse Voronoi diagram problem in graphs: given a graph G with positive edge-lengths and a collection U of subsets of vertices of V ( G ), decide whether U 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.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-020-00716-4