Abstract
We describe fully retroactive dynamic data structures for approximate range reporting and approximate nearest neighbor reporting. We show how to maintain, for any positive constant d, a set of n points in ℝd indexed by time such that we can perform insertions or deletions at any point in the timeline in O(logn) amortized time. We support, for any small constant ε > 0, (1 + ε)-approximate range reporting queries at any point in the timeline in O(logn + k) time, where k is the output size. We also show how to answer (1 + ε)-approximate nearest neighbor queries for any point in the past or present in O(logn) time.
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Goodrich, M.T., Simons, J.A. (2011). Fully Retroactive Approximate Range and Nearest Neighbor Searching. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_31
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DOI: https://doi.org/10.1007/978-3-642-25591-5_31
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