Abstract

. Given a set of n binary strings of length m each. We consider the problem of answering d--queries. Given a binary query string ff of length m, a d--query is to report if there exists a string in the set within Hamming distance d of ff. We present a data structure of size O(nm) supporting 1--queries in time O(m) and the reporting of all strings within Hamming distance 1 of ff in time O(m). The data structure can be constructed in time O(nm). A slightly modified version of the data structure supports the insertion of new strings in amortized time O(m). 1 Introduction Let W = fw 1 ; : : : ; wng be a set of n binary strings of length m each, i.e. w i 2 f0; 1g m . The set W is called the dictionary. We are interested in answering d-- queries, i.e. for any query string ff 2 f0; 1g m to decide if there is a string w i in W with at most Hamming distance d of ff. Minsky and Papert originally raised this problem in [12]. Recently a sequence of papers have considered how to solve thi...

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