Hashing of Databases with the Use of Metric Properties of the Hamming Space

Hashing of databases is considered from the point of view of information and coding theory. The records of a database are represented as binary vectors of the same length stored in the external memory of a computer. The task is formulated as follows: given a pattern and a fixed size of working memory, form the set of addresses of records that can disagree with the pattern in the number of positions smaller than the given threshold value. We use metric properties of the Hamming space and show that computational efforts needed to search for a pattern in databases can be essentially decreased by using the triangle inequality for the Hamming distances between binary vectors. Furthermore, an introduction of the Lee distance in the space containing the Hamming distances leads to a new metric space where the triangle inequality is effectively used.