In a distributed system with nodes that receive broadcast events and that should each have an up-to-date history, a problem arises when a node is restarted: Did it lose any events while it was down? If so, we need to get this history from another node that hopefully is synchronized in order to reply to future requests with the correct history.
There are ways to achieve this for systems where it is important that the history is (eventually) consistent – often by using vector clocks and time stamped messages. However, if the problem domain allows a small probability of not having a consistent history across nodes, cheaper solutions exist. By maintaining a set of hashes (a Bloom filter) per node of all the events it has received, it is possible to discover that it is out of sync by simply sending this hash to other nodes. Nodes that receive this bit-string compare it against their own hash and see if they are the same. In cases where they do not match, the node can reply with only the events that do not match the other node's hash – saving both time and bandwidth.
We have implemented a distributed chat system in Erlang using this approach. Nodes eventually get a consistent history by sending “heartbeat” synchronization events to other nodes that reply with the missing events (if any). The low-probability event of losing a chat message is acceptable, and by tuning the Bloom filter parameters we can weigh the benefit of short synchronization messages against the risk of losing messages in the chat history.