Network cardinality estimation using max consensus: The case of Bernoulli trials

Interested in scalable topology reconstruction strategies with fast convergence times, we consider network cardinality estimation schemes that use, as their fundamental aggregation mechanism, the computation of bit-wise maxima over strings. We thus discuss how to choose optimally the parameters of the information generation process under frequentist assumptions on the estimand, derive the resulting Maximum Likelihood (ML) estimator, and characterize its statistical performance as a function of the communications and memory requirements. We then numerically compare the bitwise-max based estimator against lexicographic-max based estimators, and derive insights on their relative performances in function of the true cardinality.