Presenting a result from a WADS 2007 paper by Eppstein and Goodrich
Abstract: We introduce the straggler identification problem, in which an algorithm must determine the identities of the remaining members of a set after it has had a large number of insertion and deletion operations performed on it, and now has relatively few remaining members. The goal is to do this in o(n) space, where n is the total number of identities. The straggler identification problem has applications, for example, in determining the set of unacknowledged packets in a high-bandwidth multicast data stream. We show that there is a simple randomized solution using O(d log n log(1/epsilon)) bits that can maintain a multiset and solve the straggler identification problem, tolerating false deletions, where epsilon>0 is a user-defined parameter bounding the probability of an incorrect response. This randomized solution is based on a new type of Bloom filter, which we call the invertible Bloom filter.