Dilation 2-Augmentation is fixed-parameter tractable on K_{d,d}-free graphs, while dilation 3 and weighted metric variants are W[1]- or W[2]-hard.
13 Joachim Gudmundsson and Sampson Wong
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Multivariate Exploration of Metric Dilation
Dilation 2-Augmentation is fixed-parameter tractable on K_{d,d}-free graphs, while dilation 3 and weighted metric variants are W[1]- or W[2]-hard.