Dictionary Loop-Up with Small Errors

Andrew Chi-Chih Yao, F. Frances Yao

Abstract: Let W be a set of n binary strings of length m each. We are interested in designing data structures for W that can answer d-queries quickly, that is, given a binary string α, decide whether there is any member of W within Hamming distance d of α. This problem, originally raised by Minsky and Papert [MP], remains a challenge in data structure design. In this paper, we make an initial effort towards a theoretical study of the small d case. Our main result is a data structure that achieves O(m log log n) query time with O(nm log m) space for the d = 1 case.