Fast computation by population protocols with a leader

Fast algorithms are presented for performing computations in a probabilistic population model. This is a variant of the standard population protocol model--in which finite-state agents interact in pairs under the control of an adversary scheduler--where all pairs are equally likely to be chosen for each interaction. It is shown that when a unique leader agent is provided in the initial population, the population can simulate a virtual register machine with high probability in which standard arithmetic operations like comparison, addition, subtraction, and multiplication and division by constants can be simulated in O(nlog5 n) interactions using a simple register representation or in O(nlog2 n) interactions using a more sophisticated representation that requires an extra O(nlogO(1) n)-interaction initialization step. The central method is the extensive use of epidemics to propagate information from and to the leader, combined with an epidemic-based phase clock used to detect when these ...

• Type: Journal
• Year: 2008
• Where: DC
• Authors: Dana Angluin, James Aspnes, David Eisenstat
• Keywords: DC 2001, DC 2008, Probabilistic Population Model, Standard Population Protocol, Unique Leader Agent