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arXiv · 1306.3772

Minimal Indices for Successor Search

Sarel Cohen·Amos Fiat·Moshik Hershcovitch·Haim Kaplan
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Abstract

We give a new successor data structure which improves upon the index size of the Pǎtraşcu-Thorup data structures, reducing the index size from $O(n w^{4/5})$ bits to $O(n \log w)$ bits, with optimal probe complexity. Alternatively, our new data structure can be viewed as matching the space complexity of the (probe-suboptimal) $z$-fast trie of Belazzougui et al. Thus, we get the best of both approaches with respect to both probe count and index size. The penalty we pay is an extra $O(\log w)$ inter-register operations. Our data structure can also be used to solve the weak prefix search problem, the index size of $O(n \log w)$ bits is known to be optimal for any such data structure. The technical contributions include highly efficient single word indices, with out-degree $w/\log w$ (compared to the $w^{1/5}$ out-degree of fusion tree based indices). To construct such high efficiency single word indices we device highly efficient bit selectors which, we believe, are of independent interest.

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Sarel Cohen, Amos Fiat, Moshik Hershcovitch, Haim Kaplan. 2013-06-17. Minimal Indices for Successor Search. https://arxiv.org/abs/1306.3772

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