This article presents an approach for the efficient and transparent parallelization of a large class of swarm algorithms, specifically those where the multiagent paradigm is used to implement the functionalities of bioinspired entities, such as ants and birds. Parallelization is achieved by partitioning the space on which agents operate onto multiple regions and assigning each region to a different computing node. Data consistency and conflict issues, which can arise when several agents concurrently access shared data, are handled using a purposely developed notion of logical time. This approach enables a transparent porting onto parallel/distributed architectures, as the developer is only in charge of defining the behavior of the agents, without having to cope with issues related to parallel programming and performance optimization. The approach has been evaluated for a very popular swarm algorithm, the ant-based spatial clustering and sorting of items, and results show good performance and scalability.