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Summary form only given. We propose a biologically inspired and fully-decentralized approach to the organization of computation that is based on the autonomous scheduling of strongly mobile agents on a peer-to-peer network. Our approach achieves the following design objectives: near-zero knowledge of network topology, zero knowledge of system status, autonomous scheduling, distributed computation, lack of specialized nodes. Every node is equally responsible for scheduling and computation, both of which are performed with practically no information about the system. We believe that this model is ideally suited for large-scale unstructured grids such as desktop grids. This model avoids the extensive system knowledge requirements of traditional grid scheduling approaches. Contrary to the popular master/worker organization of current desktop grids, our approach does not rely on specialized super-servers or on application-specific clients. By encapsulating computation and scheduling behavior into mobile agents, we decouple both application code and scheduling functionality from the underlying infrastructure. The resulting system is one where every node can start a large grid job, and where the computation naturally organizes itself around available resources. Through the careful design of agent behavior, the resulting global organization of the computation can be customized for different classes of applications. In a previous paper, we described a proof-of-concept prototype for an independent task application. We generalize the scheduling framework and demonstrate that our approach is applicable to a computation with a highly synchronous communication pattern, namely Cannon's matrix multiplication.