Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Efficient suffix trees on secondary storage
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Space/time trade-offs in hash coding with allowable errors
Communications of the ACM
Journal of Algorithms
Randomness conductors and constant-degree lossless expanders
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Succinct indexable dictionaries with applications to encoding k-ary trees and multisets
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Low Redundancy in Static Dictionaries with Constant Query Time
SIAM Journal on Computing
Proceedings of the 16th Conference on Foundations of Software Technology and Theoretical Computer Science
Efficient implementation of a statistics counter architecture
SIGMETRICS '03 Proceedings of the 2003 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Exact and approximate membership testers
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Analysis of a Statistics Counter Architecture
HOTI '01 Proceedings of the The Ninth Symposium on High Performance Interconnects
Journal of Algorithms
An optimal Bloom filter replacement
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Design of a novel statistics counter architecture with optimal space and time efficiency
SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
One sketch for all: fast algorithms for compressed sensing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Explicit constructions for compressed sensing of sparse signals
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Counter braids: a novel counter architecture for per-flow measurement
SIGMETRICS '08 Proceedings of the 2008 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
On the size of succinct indices
ESA'07 Proceedings of the 15th annual European conference on Algorithms
IEEE Transactions on Information Theory - Part 1
Efficient erasure correcting codes
IEEE Transactions on Information Theory
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
An analysis of the block error probability performance of iterative decoding
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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In a variety of applications, ranging from high-speed networks to massive databases, there is a need to maintain histograms and other statistics in a streaming manner. Motivated by such applications, we establish the existence of efficient source codes that are both locally encodable and locally decodable. Our solution is an explicit construction in the form of a (randomized) data structure for storing N integers. The construction uses multi-layered sparse graph codes based on Ramanujan graphs, and has the following properties: (a) the structure utilizes minimal possible space, and (b) the value of any of the integers can be read or updated in near constant time (on average and with high probability). By contrast, data structures proposed in the context of streaming algorithms and compressed sensing in recent years (e.g., various sketches) support local encodability, but not local decodability; and those known as succinct data structures are locally decodable, but not locally encodable.