Scheduling Tasks with Execution and Precedence Constraints using Longest Compatible Paths

Scheduling and resource allocation problems require numerous constraints and objectives. Latency constraints and network parameters have to be considered explicitly to produce realistic scheduling schemes. Finding an optimum scheduling algorithm is classified in the category of NP-Hard problems. Therefore, heuristic approaches are used to produce near optimal solutions with a variety of configurations. The heuristic approach presented in this paper is formulated in the framework of graph theory considering a processor network composed of a bounded number of non identical parallel processors. Every processor is able to execute only one, specific subset of tasks, having enough memory to store the communication data. The starting procedure of the algorithm uses a depth first search to find the set of all paths from source to sink. The principle procedure creates combinations of processors and task paths, seeking to allocate sets of adjacent tasks to the same compatible processor. Task selection is based on the maximum total execution time by simultaneously reducing the processor´s idle time. The paper ends with a small detailed numerical example.