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An Optimal Decentralized Algorithm for the Distributed Trigger Counting Problem

We study the distributed trigger counting problem. In this problem, we have a distributed system having n processors. These processors receive triggers from an external source. The goal is to raise an alert and report to a user when the number of triggers received by the system reaches w, where w is a user-specified input. The problem has applications in monitoring, global snapshots and other distributed settings. The main result of the paper is a randomized algorithm, which is decentralized. The message complexity of the algorithm is O(n logw); moreover, every processor receives no more than O(logw) messages. In light of lowerbounds proved in prior work, this algorithm is optimal in terms of both the message complexity and the maximum processor load.