Cell-Probe Lower Bounds for Succinct Partial Sums

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Cell-Probe Lower Bounds for Succinct Partial Sums
The partial sums problem in succinct data structures asks to preprocess an array A[1 . . n] of bits into a data structure using as close to n bits as possible, and answer queries of the form Rank(k) = k i=1 A[i]. The problem has been intensely studied, and features as a subroutine in a number of succinct data structures. We show that, if we answer Rank(k) queries by probing t cells of w bits, then the space of the data structure must be at least n + n/wO(t) bits. This redundancy/probe trade-off is essentially optimal: Patrascu [FOCS’08] showed how to achieve n+n (w/t)Ω(t) bits. We also extend our lower bound to the closely related Select queries, and to the case of sparse arrays.
Mihai Patrascu, Emanuele Viola
Added 30 Jan 2011
Updated 30 Jan 2011
Type Journal
Year 2010
Where SODA
Authors Mihai Patrascu, Emanuele Viola
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