Task Merging and Replication using Graph Rewriting

Several approaches for handling the multi-processor scheduling problem have been presented over the last decades, such as scheduling techniques, clustering techniques and task merging techniques. However, the increasing gap between processor speed and communication speed demand more accurate models of parallel computation and efficient algorithms to work under the restrictions of these models. This paper presents a method for merging tasks in a task graph in order to increase its granularity, i.e. the ratio between communication and execution cost of the task graph. The parallel computation model used is a simplified version of the LogP model, where only the communication speed and the communication latency, is considered. The method uses a set of graph rewrite rules, where each rule merges two or more tasks into a single task. The rules are applied as in a graph rewrite system, until no further transformations are possible. The rewrite rules are defined for a few simple patterns for merging tasks. For instance, the simplest one, called singlechildmerge, states that two tasks connected by an edge can be merged if the condition that the parent task only has this one child and the child task only has one parent is fulfilled. Another example is a rewrite rule involving task duplication, where a split node is replicated and merged into each of its children. The task merging approach using graph rewrite rules has been tested on automatically generated simulation code from an equation based simulation language called Modelica. The task graphs of the tested examples are reduced substantially in size, both increasing the granularity of the task graph and decreasing the demands on an efficient scheduling algorithm.