The GCA-w Massively Parallel Model

Abstract

We introduce the GCA-w model (Global Cellular Automata with write access) that is an extension of the GCA (Global Cellular Automata) model, which is in turn an extension of the cellular automata (CA) model. All three models are called "massively parallel" because the models are based on cells that are updated synchronously in parallel. In the CA model, the cells have static links to their local neighbors whereas in the GCA model, the links are dynamic to any global neighbor. In both models, the access is “read-only”. Thereby no write conflict can occur which reduces the complexity of the model and its implementation. The GCA model can be used for many parallel problems that can be described with a changing global (or locally restricted) neighborhood. The main restriction of the GCA model is the forbidden write access to neighboring cells. Although the write access can be emulated in O(log n) time this slowdown is not desired in practical applications. Therefore, the GCA-w model was developed. The GCA-w model allows to change the state of the own cell as well as the states of the neighboring cells. Thereby parallel algorithms can be executed faster and the activity of the cells can be controlled in order, e.g., to reduce power consumption or to use inactive cells for other purposes. The application of the GCA-w model is demonstrated for some parallel algorithms: pointer inversion, sorting with pointers, synchronization and Pascal’s triangle. In addition, a hardware architecture is outlined which can execute this model.