A qualitative method to optimise false positive occurrences for the in-packet Bloom filter forwarding mechanism

Bloom filters have been recently proposed as an efficient multicast forwarding mechanism for the information centric topic-based publish/subscribe network proposed within the framework of the PSIRP project. Although such mechanism presents several advantages, as for instance very simple forwarding decisions and small forwarding tables, one of the limitations is the possibility of false positive occurrences during the forwarding decisions. This results in packets to be sent along unexpected links and the consequently wastage of network bandwidth among other effects. Therefore, its frequency must be minimized. One of the crucial points to reduce false positives in Bloom Filters is carefully select the number of hash functions utilized to create them. In this paper, we propose a mathematical analysis of the false positives in the whole network with respect to the number of hash functions. In particular, the number of hash functions correspondent to a minimum of false positive for the whole network is evaluated. Results from the mathematical analysis are compared with numerical analysis.