2008/02/11 by Ronald de Wolf, de Wolf, Ronald
Biochemistry, Genetics and Molecular Biology · Computer Science · #Advanced Data Storage Technologies #Cryptography and Data Security #DNA and Biological Computing #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #cs.DS
paper · pdf · doi:10.48550/arxiv.0802.1471
15 pages LaTeX; an abridged version will appear in the Proceedings of the STACS 2009 conference
openalex publication_date 2008/02/11 · arxiv created 2008/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.