## Efficient approximate dictionary look-up over small alphabets (2005)

Citations: | 3 - 1 self |

### BibTeX

@TECHREPORT{Arslan05efficientapproximate,

author = {Abdullah N. Arslan},

title = {Efficient approximate dictionary look-up over small alphabets},

institution = {},

year = {2005}

}

### OpenURL

### Abstract

Given a dictionary W consisting of n binary strings of length m each, a d-query asks if there exists a string in W within Hamming distance d of a given binary query string q. The problem was posed by Minsky and Papert in 1969 [10] as a challenge to data structure design. Efficient solutions have been developed only for the special case when d = 1 (the 1-query problem). We assume the standard RAM model of computation, and consider the case of the problem when alphabet size is arbitrary but finite, and d is small. We preprocess the dictionary, and construct an edge-labelled tree with bounded branching factor, and height. We present an algorithm to answer dictionary look-up within given distance d of a given query string q. The algorithm is efficient when the alphabet size is small, or the dictionary is sparse. In particular, for the d-query problem the algorithm takes time O(m(log 4/3 n − 1) d (log 2 n) d+1). This is an improvement over previously known algorithms for the d-query problem when d> 1. We also generalize the results for the case of the problem when edit distances are used. The algorithm can be modified such that it allows for words of different lengths as well as different lengths of query strings. 1