Abstract
Let \(w \in {\mathbb {N}}\) and \(U = \{0, 1, \dots , 2^w-1\}\) be a bounded universe of w-bit integers. We present a dynamic data structure for predecessor searching in U. Our structure needs \(O(\log \log \varDelta )\) time for queries and \(O(\log \log \varDelta )\) expected time for updates, where \(\varDelta \) is the difference between the query element and its nearest neighbor in the structure. Our data structure requires linear space. This improves a result by Bose et al. [CGTA, 46(2), pp. 181–189].
The structure can be applied for answering approximate nearest neighbor queries in low dimensions and for dominance queries on a grid.
Supported in part by DFG project MU/3501-1.
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Ehrhardt, M., Mulzer, W. (2017). Delta-Fast Tries: Local Searches in Bounded Universes with Linear Space. In: Ellen, F., Kolokolova, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2017. Lecture Notes in Computer Science(), vol 10389. Springer, Cham. https://doi.org/10.1007/978-3-319-62127-2_31
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DOI: https://doi.org/10.1007/978-3-319-62127-2_31
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