Error-Correcting Data Structures
Abstract
We study data structures in the presence of adversarial noise. We want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object, even if the data structure has been corrupted by a constant fraction of errors. This new model is the common generalization of (static) data structures and locally decodable error-correcting codes. The main issue is the tradeoff between the space used by the data structure and the time (number of probes) needed to answer a query about the encoded object. We prove a number of upper and lower bounds on various natural error-correcting data structure problems. In particular, we show that the optimal length of error-correcting data structures for the Membership problem (where we want to store subsets of size s from a universe of size n) is closely related to the optimal length of locally decodable codes for s-bit strings.
Cite
@article{arxiv.0802.1471,
title = {Error-Correcting Data Structures},
author = {Ronald de Wolf},
journal= {arXiv preprint arXiv:0802.1471},
year = {2008}
}
Comments
15 pages LaTeX; an abridged version will appear in the Proceedings of the STACS 2009 conference