Realizability of Delaunay triangulations
Information Processing Letters
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Efficient Data Reduction for DOMINATING SET: A Linear Problem Kernel for the Planar Case
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Boltzmann Samplers for the Random Generation of Combinatorial Structures
Combinatorics, Probability and Computing
A refined search tree technique for Dominating Set on planar graphs
Journal of Computer and System Sciences
Generating labeled planar graphs uniformly at random
Theoretical Computer Science
Uniform random sampling of planar graphs in linear time
Random Structures & Algorithms
Experimental evaluation of a tree decomposition-based algorithm for vertex cover on planar graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
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We survey several planar graph generators that were selected according to availability, theoretical interest, easiness of implementation and efficiency. We experimentally study graph properties that allow for a basic classification of the generators. This analysis is extended by means of advanced algorithmical behavior on the generated graphs, in particular kernelization of fixed-parameter tractable problems. We will see the major influence of instance selection on algorithmic behavior. This selection has been disregarded in several publications, which deduce general results from non-representative data sets. Altogether, this study helps experimenters to carefully select sets of planar graphs that allow for a meaningful interpretation of their results.