DMCA
EFFICIENT AND ERROR-CORRECTING DATA STRUCTURES FOR MEMBERSHIP AND POLYNOMIAL EVALUATION
Cached
Download Links
| Venue: | SUBMITTED TO THE SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE |
| Citations: | 5 - 1 self |
BibTeX
@MISC{Chen_efficientand,
author = {Victor Chen and Elena Grigorescu and Ronald de Wolf},
title = {EFFICIENT AND ERROR-CORRECTING DATA STRUCTURES FOR MEMBERSHIP AND POLYNOMIAL EVALUATION},
year = {}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
We construct efficient data structures that are resilient against a constant fraction of adversarial noise. Our model requires that the decoder answers most queries correctly with high probability and for the remaining queries, the decoder with high probability either answers correctly or declares “don’t know.” Furthermore, if there is no noise on the data structure, it answers all queries correctly with high probability. Our model is the common generalization of an error-correcting data structure model proposed recently by de Wolf, and the notion of “relaxed locally decodable codes” developed in the PCP literature. We measure the efficiency of a data structure in terms of its length (the number of bits in its representation), and query-answering time, measured by the number of bit-probes to the (possibly corrupted) representation. We obtain results for the following two data structure problems: • (Membership) Store a subset S of size at most s from a universe of size n such that membership queries can be answered efficiently, i.e., decide if a given element from the universe is in S. We construct an error-correcting data structure for this problem with length nearly linear in s log n that answers membership queries with O(1) bit-probes. This nearly matches the asymptotically optimal parameters for the noiseless case: length O(s log n) and one bit-probe, due to
Keyphrases
high probability data structure adversarial noise optimal parameter query-answering time answer membership query pcp literature efficient data structure constant fraction membership query noiseless case common generalization error-correcting data structure model data structure problem decodable code error-correcting data structure
