Process discovery is an approach to extract process models from event logs. Given the distributed nature of modern information systems, event logs are likely to be distributed across different physical machines. Map-Reduce is a scalable approach for efficient computations on distributed data. In this paper we present Map-Reduce implementations of two well-known process mining algorithms to take advantage of the scalability of the Map-Reduce approach. We present the design of a series of mappers and reducers to compute the log-based ordering relations from distributed event logs. These can then be used to discover a process model. We provide experimental results that show the performance and scalability of our implementations.