Red-blue point separation for points on a circle

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dc.contributor.author Misra, Neeldhara
dc.contributor.author Mittal, Harshil
dc.contributor.author Sethia, Aditi
dc.date.accessioned 2020-05-27T14:12:54Z
dc.date.available 2020-05-27T14:12:54Z
dc.date.issued 2020-05
dc.identifier.citation Misra, Neeldhara; Mittal, Harshil and Sethia, Aditi, "Red-blue point separation for points on a circle", arXiv, Cornell University Library, DOI: arXiv:2005.06046, May 2020. en_US
dc.identifier.uri http://arxiv.org/abs/2005.06046
dc.identifier.uri https://repository.iitgn.ac.in/handle/123456789/5435
dc.description.abstract Given a set R of red points and a set B of blue points in the plane, the Red-Blue point separation problem asks if there are at most k lines that separate R from B, that is, each cell induced by the lines of the solution is either empty or monochromatic (containing points of only one color). A common variant of the problem is when the lines are required to be axis-parallel. The problem is known to be NP-complete for both scenarios, and W[1]-hard parameterized by k in the former setting and FPT in the latter. We demonstrate a polynomial-time algorithm for the special case when the points lie on a circle. Further, we also demonstrate the W-hardness of a related problem in the axis-parallel setting, where the question is if there are p horizontal and q vertical lines that separate R from B. The hardness here is shown in the parameter p.
dc.description.statementofresponsibility by Neeldhara Misra, Harshil Mittal and Aditi Sethia
dc.language.iso en_US en_US
dc.publisher Cornell University Library en_US
dc.title Red-blue point separation for points on a circle en_US
dc.type Pre-Print en_US
dc.relation.journal arXiv


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