We propose a model called priority branching trees (pBT ) for backtracking and dynamic
programming algorithms. Our model generalizes both the priority model of Borodin, Nielson
and Rackoff, as well as a simple dynamic programming model due to Woeginger, and hence
spans a wide spectrum of algorithms. After witnessing the strength of the model, we then
show its limitations by providing lower bounds for algorithms in this model for several classical
problems such as Interval Scheduling, Knapsack and Satisfiability.