In this paper, we present an efficient causal algorithm that can be used in multicast communication environments, in particular the overlapping multi-channel case, where a participant can belong to and communicate through more than one multicast channel. The causal algorithm is built on the paradigm of group communication. The groups are established according to the participant channel subscription. In order to reduce the amount of control information (CI), we propose an extension of the immediate dependency relation (IDR), which was introduced by Peterson in the context of one group. This IDR extension allows us to define necessary and sufficient CI to ensure causal delivery in a multi-group environment. We show that through the use of the IDR extension, we reduce the amount of CI sent per message without imposing restrictions on interaction or execution (e.g. network topology, rediffusion servers, execution models, etc.). These characteristics allow our algorithm to be suitable for use in large distributed decentralised systems. We show the efficiency of our causal algorithm in terms of the overhead timestamped per message.