SIAM Journal on Computing
On the cell probe complexity of membership and perfect hashing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Low Redundancy in Static Dictionaries with Constant Query Time
SIAM Journal on Computing
SIAM Journal on Computing
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
The complexity of hardness amplification and derandomization
The complexity of hardness amplification and derandomization
A simple optimal representation for balanced parentheses
Theoretical Computer Science
On dynamic bit-probe complexity
Theoretical Computer Science
Parallel repetition: simplifications and the no-signaling case
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Hardness amplification proofs require majority
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Cell probe lower bounds for succinct data structures
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Changing base without losing space
Proceedings of the forty-second ACM symposium on Theory of computing
Cell-probe lower bounds for succinct partial sums
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Hardness Amplification Proofs Require Majority
SIAM Journal on Computing
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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 Patrascu (FOCS 2008), later refined with Thorup, where u ≤ (log_2 3)n + n/2Ω(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 fundamental problems; we obtain them drawing on ideas used in lower bounds for locally decodable codes.