# Cristian's algorithm

Cristian's algorithm (introduced by Flaviu Cristian in 1989)[1] is a method for clock synchronization which can be used in many fields of distributive computer science but is primarily used in low-latency intranets. Cristian observed that this simple algorithm is probabilistic, in that it only achieves synchronization if the round-trip time (RTT) of the request is short compared to required accuracy. It also suffers in implementations using a single server, making it unsuitable for many distributive applications where redundancy may be crucial.

## The algorithm

Cristian's algorithm works between a process P, and a time server S — connected to a source of UTC (Coordinated Universal Time). Put simply:

1. P requests the time from S
2. After receiving the request from P, S prepares a response and appends the time T from its own clock.
3. P then sets its time to be T + RTT/2

This method assumes that the RTT (Round Trip Time) is split equally between request and response, which may not always be the case but is a reasonable assumption on a LAN connection.

Further accuracy can be gained by making multiple requests to S and using the response with the shortest RTT.

We can estimate the accuracy of the system as follows. Let min be the minimum time to transmit a message one-way. The earliest point at which S could have placed the time T, was min after P sent its request. Therefore, the time at S, when the message by P is received, is in the range (T + min) to (T + RTT - min). The width of this range is (RTT - 2*min). This gives an accuracy of (RTT/2 - min).