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.

Distributed Identification of the Most Critical Node for Average Consensus

“…3. The results suggest that the conservative bound in (8) can be large in many cases (e.g., for node 28, is 1.2465 while the true estimation error is 0.02094). However, in some extreme cases (e.g., when close to 1) the bound (8) outperforms the second bound in (9).…”

“…Here can be chosen as the network diameter and is assumed known to every node. This assumption is reasonable because network diameter can be obtained in fully distributed ways [8], [36]. As for choosing the threshold , we only need to guarantee that stored in every node will not shrink to 0 (machine zero) in steps if starting at , i.e., As for , we only need to ensure a proper length of (not too large), which is very loose.…”

Fast distributed estimation of empirical mass functions over anonymous networks

“…Considering a certain agent i, the set of p We notice that estimator (11) has strong similarities with the size estimators proposed in [26], [27], [28].…”

On Distributed Cardinality Estimation: Random Arcs Recycled

“…Building on these solutions several distributed size estimation protocols dedicated to wireless systems have been proposed recently (e.g., [3,5,6,7,19,20]). However, these protocols implicitly assume that a communication framework is already established and hide the complexity of the underlying implementation.…”

“…Several distributed size estimation algorithms dedicated to ad hoc wireless systems have been proposed recently, e.g. [3,5,19,20,21]. Most of them could be also easily adapted to estimate the size of a node's neighborhood.…”