Sparse structured associative memories as efficient set-membership data structures

We study the use of sparse structured associative memories as a memory-efficient and computationally-efficient data structure for representing a set of elements when one wishes to perform set-membership queries and some errors (false positives) are tolerable. Associative memories, when viewed as representing a set, enjoy a number of interesting properties, including that set membership queries can be carried out even when the input (query element) is only partially known or is partially corrupted. The associative memories considered here (initially proposed in [Gripon and Berrou, 2011]) encode the set in the edge structure of a graph. In this paper we generalize this construction to encode the set in the edge structure of a hypergraph. We derive bounds on the false positive rates (the probability that the associative memory erroneously declares that an element is in the stored set when it, in fact, was not). Interestingly, the proposed structures enjoy many of the same properties as Bloom filters (e.g., they have zero false negative rate, the time to perform an insert and lookup does not depend on the number of elements stored, and the false positive rate can be reduced by using additional memory for storage), while also offering the properties of associative memories (allowing for queries on partial or corrupted inputs).