Bloom filters and their applications

The bloom filters, as a new approach to hashing, were firstly presented by Burton Bloom [Blo70]. He considered the task of presenting a set as a sequence of bits, which is called hash code of the set. In comparison with the conventional hash-coding method, author offered another technique allowing to get more concise presentation of the set, but with some errors. There are applications in which errors with some allowable level are permitted. Allowing the possibility of these errors, we can reduce a space required for presentating a set in such applications. An example is a spell-checking system where we allow some amount of mistakes in presentation of dictionary. We begin with the theory of Bloom filters. Subsection 2.1 deals with conventional hash-coding method. Firstly we introduce a hash-coding method, where no errors are permitted and then we explore how space requirements can be reduced by allowing errors in the system. In subsection 2.2 we give the definition of Bloom filter and compare this method with the previous one. All material presented in this section is based on original Bloom’s paper [Blo70]. In subsection 2.3 we present generalization of Bloom filters for presentation of multi-set proposed in [CM03]. The main advantages of new concept are presented. In the section 3 we consider one application of bloom filters. It deals with the so called differential file access problem. This problem usually arises in systems where simulteneous access to a file is required. The bloom filters are used there for a concise presentation of a differential file. The material of this section is based on [Mul83, Gre82]