Adding Networks

Abstract

An adding network is a distributed data structure that supports a concurrent, lock-free, low-contention implementation of a fetchℰadd counter; a counting network is an instance of an adding network that supports only fetchℰincrement. We present a lower bound showing that adding networks have inherently high latency. Any adding network powerful enough to support addition by at least two values a and b, where |a| > |b| > 0, has sequential executions in which each token traverses Ω(n/c) switching elements, where n is the number of concurrent processes, and c is a quantity we call one-shot contention; for a large class of switching networks and for conventional counting networks the one-shot contention is constant. On the contrary, counting networks have O(log n) latency [4,7.

This bound is tight. We present the first concurrent, lock-free, lowcontention networked data structure that supports arbitrary fetch&add operations.

This work has been accepted for publication as a brief announcement in the 20th Annual ACM Symposium on Principles of Distributed Computing, Newport, Rhode Island, August 2001. Part of the work of the first author was performed while affiliating with the Max-Planck Institut für Informatik, Saarbrücken, Germany, and while visiting the Department of Computer Science, Brown University, Providence, USA.