Efficient and Error-Correcting Data Structures for Membership and Polynomial Evaluation

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 s...

• Type: Conference
• Year: 2010
• Where: STACS
• Authors: Victor Chen, Elena Grigorescu, Ronald de Wolf
• Keywords: STACS 2010, Theoretical Computer Science