An optimal distributed trigger counting algorithm for large-scale networked systems

Distributed trigger counting (DTC) is a problem related to the detection of w triggers with n nodes in large-scale distributed systems that have general characteristics of complex adaptive systems. The triggers come from an external source, and no a priori information about the triggers is given. DTC algorithms can be used for distributed monitoring and global snapshots. When designing an efficient DTC algorithm, the following goals should be considered: minimizing the overall message complexity and distributing the loads for detecting triggers among nodes. In this paper, we propose a randomized algorithm called TreeFill, which satisfies the message complexity of O(nlog(w/n)) with high probability. The maximum number of received messages to detect w triggers in each node is O(log(w/n)) with high probability. These results satisfy the lower bounds of DTC problems. We prove the upper bounds of TreeFill. The performance of TreeFill is also evaluated by means of an agent-based simulation using NetLogo. The simulation results show that TreeFill uses about 54-69% of the messages used in a previous work called CoinRand. The maximum number of received messages in each node of TreeFill is also smaller than that in the previous work.