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A novel compression scheme for compressing the outcome of $n$ independentBernoulli trials is introduced and analysed. The resulting algorithm,BernoulliZip, is a fast and near-optimal method to produce prefix codes for aBernoulli process. BernoulliZip's main principle is to first represent thenumber of 1s in the sequence and then specify the sequence. The application ofBernoulliZip on compressing Erdos-Renyi graphs is explored.

BernoulliZip: a Compression Algorithm for Bernoulli Processes and Erdos-Renyi Graphs