On a parity based group testing algorithm

In traditional Combinatorial Group Testing the problem is to identify up to d defective items from a set of n items on the basis of group tests. In this paper we describe a variant of the group testing problem above, which we call parity group testing. The problem is to identify up to d defective items from a set of n items as in the classical group test problem. The main difference is that we check the parity of the defective items in a subset. The test can be applied to an arbitrary subset of the n items with two possible outcomes. The test is positive if the number of defective items in the subset is odd, otherwise it is negative. In this paper we extend Hirschberg et al.’s method to the parity group testing scenario

Bloom Filter with a False Positive Free Zone

Bloom filters and their variants are widely used as space-efficient probabilistic data structures for representing sets and are very popular in networking applications. They support fast element insertion and deletion, along with membership queries with the drawback of false positives. Bloom filters can be designed to match the false positive rates that are acceptable for the application domain. However, in many applications, a common engineering solution is to set the false positive rate very small and ignore the existence of the very unlikely false positive answers. This paper is devoted to close the gap between the two design concepts of unlikely and not having false positives. We propose a data structure called EGH filter that supports the Bloom filter operations, and besides, it can guarantee false positive free operations for a finite universe and a restricted number of elements stored in the filter. We refer to the limited universe and filter size as the false positive free zone of the filter. We describe necessary conditions for the false-positive free zone of a filter. We then generalize the filter to support the listing of the elements through the use of counters rather than bits. We detail networking applications of the filter and discuss potential generalizations. We evaluate the performance of the filter in comparison with the traditional Bloom filters. We also evaluate the price in terms of memory that needs to be paid to guarantee real false positive-free operations for having a deterministic Bloom filter-like behavior. Our data structure is based on recently developed combinatorial group testing techniques