Over the last few years energy minimization has emerged as an indispensable tool in computer vision. The primary reason for this rising popularity has been the successes of efficient graph cut based minimization algorithms in solving many low level vision problems such as image segmentation, object reconstruction, image restoration and disparity estimation. The scale and form of computer vision problems introduce many challenges in energy minimization. In this chapter we address the problem of efficient and exact minimization of groups of similar functions which are known to be solvable in polynomial time. We will present a novel dynamic algorithm for minimizing such functions. This algorithm reuses computation from previous problem instances to solve new instances resulting in a substantial improvement in the running time. We will present the results of using this approach on the problems of interactive image segmentation, image segmentation in video, human pose estimation and segmentation, and measuring uncertainty of solutions obtained by minimizing energy functions.