Dictionary Look-Up with One Error

LetWbe a set ofnbinary strings of lengthmeach. We are interested in designing data structures forWthat can answerd-queriesquickly; that is, given in a binary string ?, decide whether there is any member ofWwithin Hamming distancedof ?. The problem, originally raised by Minsky and Papert, remains a challenge in data structure design. In this paper, we make an initial effort toward a theoretical study of the smalldcase. Our main result is a data structure that achievesO(mloglogn) query time withO(nmlogm) space for thed=1 case.

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