Point Location in Dynamic Planar Subdivisions

03/12/2018

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by   Eunjin Oh, et al.

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We study the point location problem on dynamic planar subdivisions that allows insertions and deletions of edges. In our problem, the underlying graph of a subdivision is not necessarily connected. We present a data structure of linear size for such a dynamic planar subdivision that supports sublinear-time update and polylogarithmic-time query. Precisely, the amortized update time is O(√(n) n( n)^3/2) and the query time is O( n( n)^2), where n is the number of edges in the subdivision. This answers a question posed by Snoeyink in the Handbook of Computational Geometry. When only deletions of edges are allowed, the update time and query time are just O(α(n)) and O( n), respectively.