纠错数据结构
Error-Correcting Data Structures
摘要：
我们研究了对抗性噪声存在下的数据结构。我们希望将给定的对象编码为简洁的数据结构，使我们能够有效地回答有关该对象的特定查询，即使数据结构已被恒定的错误率损坏。这种新模型是（静态）数据结构和局部可解码的纠错码的共同推广。主要问题是数据结构使用的空间和回答关于编码对象的查询所需的时间（探测器的数量）之间的权衡。我们证明了各种自然纠错数据结构问题的一些上界和下界。特别是，我们表明，最佳长度的纠错数据结构的成员资格问题（我们要存储的子集大小为s从宇宙大小为n）是密切相关的最佳长度的本地可解码代码的s-位串。
英文摘要：
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.
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