LOTs (Leaf Only Trees) Fast Efficient and Robust In-Network Computations
Andre Allevena, University of Waterloo

The need for efficient computation of functions of global state lies at the heart of a wide range of problems in distributed systems. Examples include load balancing, leader election and barrier synchronisation, distributed file system maintenance, sensor fusion, coordinated intrusion detection, and top-K queries in stream-oriented databases. More precisely, we wish to compute a function $g$ on the values held by the nodes. In practice, computing such functions involves in-network computation of partial functions, to avoid the overhead of exchanging Ω(n) sized messages.

Epidemic (or gossip) algorithms are known as the most robust and efficient way to disseminate information in a network. However, they suffer from the "double counting" problem. Solutions to this problem either make gossip brittle or depend on variants of the Flajolet-Martin algorithm, which results in errors of up to 50%.

In this paper, we present the first efficient, accurate and robust algorithm for in-network computation of functions of global state. We provide a simple abstraction of a B-tree on which arbitrary functions can be evaluated. The scheme is fast and efficient: it terminates in O(ln n) communication rounds and every node sends most of its messages to nearby nodes. Most useful functions like sum or approximate histogram can be embedded in the tree, resulting in messages of size O(ln n). For functions that need to be distorted to be embedded into the tree, the price is not loss of precision but larger messages, of size proportional to the degree of distortion. Our analysis includes bounds on degree of load imbalance and tolerance of node failures.

Joint work with S. Keshav.