# PTAS for Steiner Tree on Map Graphs

@article{Byrka2019PTASFS, title={PTAS for Steiner Tree on Map Graphs}, author={Jaroslaw Byrka and Mateusz Lewandowski and Syed Mohammad Meesum and Joachim Spoerhase and Sumedha Uniyal}, journal={ArXiv}, year={2019}, volume={abs/1912.00717} }

We study the Steiner tree problem on map graphs, which substantially generalize planar graphs as they allow arbitrarily large cliques. We obtain a PTAS for Steiner tree on map graphs, which builds on the result for planar edge weighted instances of Borradaile et al. The Steiner tree problem on map graphs can be casted as a special case of the planar node-weighted Steiner tree problem, for which only a 2.4-approximation is known. We prove and use a contraction decomposition theorem for planar… CONTINUE READING

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