Scheduling Applications of DAGs

Task scheduling is a fundamental function of the operating systems. Hardware-In-Loop (HIL) testing that employs test vectors is a common testing methodology for embedded systems. The modeling of tasks in operating systems and test cases in HIL testing can be viewed in a unified manner as scheduling problems. Both of these problems can be modeled by directed acyclic graphs, i.e. DAGs. The stretch of a DAG G is the length of longest path from u to v in G, for all choices of (u, v) is an element of V denoted by Delta(G). The stretch of a DAG can be computed in O(vertical bar V vertical bar+vertical bar E vertical bar) time. Layering refers to a consistent assignment of level numbers to all vertices of a DAG. An efficient algorithm that layers a given DAG is designed with a running time of O(vertical bar V vertical bar + vertical bar E vertical bar). We show how to efficiently solve some scheduling problems with the help of layering.