In brief summary, the following results were presented in this work: A linear time approach was developed to find register requirements for any specified CS schedule or filled MRT. An algorithm was developed for finding register requirements for any kernel that has a dependence graph that is acyclic and has no data reuse on machines with depth independent instruction templates. We presented an efficient method of estimating register requirements as a function of pipeline depth. We developed a technique for efficiently finding bounds on register require ments as a function of pipeline depth....