Folding and Unfolding Bloom Filters - An off-Line Planing and on-Line Optimisation

Last decade is characterised by the convergence of pervasive technologies including wireless communication, smart devices and the Internet. The resulting Internet of the things enables not-only users but also things to access resource anywhere, anytime. In practice, data is ubiquitously flowed relying on global wireless connectivity (e.g., 3G) or on ad hoc-based local area networking, as enabled by e.g., IEEE 802.15.4 protocols. One key limitation of those networks remains the limited bandwidth and energy. In this context, early-stage data and resource discovery should be provided so as to provide efficient data dissemination [12]. A Bloom filter is a spaceefficient structure (namely a vector of bits) that is dedicated to the representation of a set and designed so as to support efficient membership queries. It distinguished itself by the fact that the time associated with querying a membership is independent of the number of elements stored in the Bloom filter as well the size of the Bloom filter. In a nutshell, the Bloom filter works as follows. An element intended to be added to the Bloom filter is first hashed. Then, the output is used to flip to 1 the bit at the related position in the Bloom filter. Typically, k > 1 hash functions are used. In order to check whether an element is stored in the Bloom filter, the queried element is hashed and if the bits at the related position are set to 1 in the Bloom filter, then, this element is stored. It is worth to mention that false negatives are not encountered. Nevertheless, the approximate nature of Bloom filter implies that false positives might take place. The probability of false positive depends of (i) the Bloom filter size, (ii) the number of hash functions and (iii) the number of elements that are stored. Keeping to a minimum the false positive rate requires the dynamically adaptation of the number of hash functions or/and the Bloom filter size. Further attempts to increase the size of the Bloom filter appeared in the literature. The basic idea consists in creating a set of Bloom filters [5], [15], [1]. As a side effect, a membership request becomes a function of the size of this set. While these methods deal with the increase of the Bloom filter size, the related decrease is neglected. An alternative [6] consists in partitioning the Bloom filter in k disjoint sub-ranges wherein