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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Minimal Indices for Successor Search
(Extended Abstract)
verfasst von : Sarel Cohen, Amos Fiat, Moshik Hershcovitch, Haim Kaplan
Erschienen in: Mathematical Foundations of Computer Science 2013
Verlag: Springer Berlin Heidelberg
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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.