  Maximal Independent Set selection is a fundamental problem in distributed
computing. A novel probabilistic algorithm for this problem has recently been
proposed by Afek et al, inspired by the study of the way that developing cells
in the fly become specialised. The algorithm they propose is simple and robust,
but not as efficient as previous approaches: the expected time complexity is
O(log^2 n). Here we first show that the approach of Afek et al cannot achieve
better efficiency than this across all networks, no matter how the probability
values are chosen. However, we then propose a new algorithm that incorporates
another important feature of the biological system: adapting the probabilities
used at each node based on local feedback from neighbouring nodes. Our new
algorithm retains all the advantages of simplicity and robustness, but also
achieves the optimal efficiency of O(log n) expected time.
