Abstract
The linear-time ham-sandwich cut algorithm of Lo, Matoušek, and Steiger for bi-chromatic finite point sets in the plane works by appropriately selecting crossings of the lines in the dual line arrangement with a set of well-chosen vertical lines. We consider the setting where we are not given the coordinates of the point set, but only the orientation of each point triple (the order type) and give a deterministic linear-time algorithm for the mentioned sub-algorithm. This yields a linear-time ham-sandwich cut algorithm even in our restricted setting. We also show that our methods are applicable to abstract order types.
Supported by the ESF EUROCORES programme EuroGIGA - ComPoSe. A.P. is supported by Austrian Science Fund (FWF): I 648-N18. Part of this work was presented in the PhD thesis [25] of the second author.
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Felsner, S., Pilz, A. (2014). Ham-Sandwich Cuts for Abstract Order Types. In: Ahn, HK., Shin, CS. (eds) Algorithms and Computation. ISAAC 2014. Lecture Notes in Computer Science(), vol 8889. Springer, Cham. https://doi.org/10.1007/978-3-319-13075-0_57
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DOI: https://doi.org/10.1007/978-3-319-13075-0_57
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