Connection of Optimal Stopping Time to s-t Cut Problems on Trees

We present a method to transform any optimal stopping time problem with an underlying tree structure into an s-t min-cut problem on the same tree but with modified capacities, the details of which are lacking in existing optimal stopping time research. We also show that any s-t min/max-cut problem on a tree has an equivalent optimal stopping problem formulation. We provide a dynamic programming algorithm to solve this problem and also perform a sensitivity analysis on it. Our results imply that the s-t max-cut problem on a tree can be solved using an algorithm with runtime that is linear in the tree size.