Feedback from nature: an optimal distributed algorithm for maximal independent set selection

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(log2 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 global probability values are chosen. However, we then propose a new algorithm that incorporates another important feature of the biological system: the probability value at each node is adapted using 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. The new algorithm also has only a constant message complexity per node.