Extrema propagation: Fast distributed estimation of sums and network sizes

Abstract—Aggregation of data values plays an important role on distributed computations, in particular, over peer-to-peer and sensor networks, as it can provide a summary of some global system property and direct the actions of self-adaptive distributed algorithms. Examples include using estimates of the network size to dimension distributed hash tables or estimates of the average system load to direct load balancing. Distributed aggregation using nonidempotent functions, like sums, is not trivial as it is not easy to prevent a given value from being accounted for multiple times; this is especially the case if no centralized algorithms or global identifiers can be used. This paper introduces Extrema Propagation, a probabilistic technique for distributed estimation of the sum of positive real numbers. The technique relies on the exchange of duplicate insensitive messages and can be applied in flood and/or epidemic settings, where multipath routing occurs; it is tolerant of message loss; it is fast, as the number of message exchange steps can be made just slightly above the theoretical minimum; and it is fully distributed, with no single point of failure and the result produced at every node. Index Terms—Aggregation, network size estimation, distributed sums, probabilistic estimation, self-configuration. Ç