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arXiv · 2405.15088

(Worst-Case) Optimal Adaptive Dynamic Bitvectors

Gonzalo Navarro
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Abstract

While operations {\em rank} and {\em select} on static bitvectors can be supported in constant time, lower bounds show that supporting updates raises the cost per operation to $\Theta(\log n/ \log\log n)$ on bitvectors holding $n$ bits. This is a shame in scenarios where updates are possible but uncommon. We develop a representation of bitvectors that we call adaptive dynamic bitvector, which uses the asymptotically optimal $n+o(n)$ bits of space and, if there are $q$ queries per update, supports all the operations in $O(\log(n/q)/\log\log n)$ amortized time. Further, we prove that this time is \new{worst-case} optimal in the cell probe model. We describe a large number of applications of our representation to other compact dynamic data structures.

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Gonzalo Navarro. 2024-05-23. (Worst-Case) Optimal Adaptive Dynamic Bitvectors. https://arxiv.org/abs/2405.15088

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