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. 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. The main issue is the trade-off between these two. This new model is the common generalization of (static) data structures and locally decodable error-correcting codes (LDCs). 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 $t$-probe error-correcting data structures for the Membership problem (where we want to store subsets of size $s$ from a universe of size $n$ such that membership queries can be answered effic...
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