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2009
ACM

Bit-probe lower bounds for succinct data structures

9 years 3 months ago
Bit-probe lower bounds for succinct data structures
We prove lower bounds on the redundancy necessary to represent a set S of objects using a number of bits close to the information-theoretic minimum log2 |S|, while answering various queries by probing few bits. Our main results are: ? To represent n ternary values t {0, 1, 2}n in terms of u bits b {0, 1}u while accessing a single value ti {0, 1, 2} by probing q bits of b, one needs u (log2 3)n + n/2O(q) . This matches an exciting representation by Patra?scu (FOCS 2008), later refined with Thorup, where u (log2 3)n + n/2(q). We also note that results on logarithmic forms imply the lower bound u (log2 3)n + n/ logO(1) n if we access ti by probing one cell of log n bits. ? To represent sets of size n/3 from a universe of n elements in terms of u bits b {0, 1}u while answering membership queries by probing q bits of b, one needs u log2 n n/3 + n/2O(q) - log n. Both results above hold even if the probe locations are determined adaptively. Ours are the first lower bounds for these f...
Emanuele Viola
Added 23 Nov 2009
Updated 23 Nov 2009
Type Conference
Year 2009
Where STOC
Authors Emanuele Viola
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