We consider the following optimal decision problem. Let $\{(X_i,Y_i)\}_{i\geq 1}$
be a sequence of pairs of random variables, and let $S$ be a stopping time with 
respect to $\{X_i\}_{i\geq 1}$. For a fixed $k\geq 1$, we consider the problem of
 finding a stopping time $T\leq k$ with respect to $\{Y_i\}_{i\geq 1}$ that 
optimally tracks $S$, in the sense that $T$ minimizes the average 
{\emph{reaction time}} $E \max\{0,T-S\}$, while keeps the
{\emph{false-alarm probability}} $P(T<S)$ below a given threshold $\alpha \in
[0,1]$.  This problem has applications in several areas, such as in communication, 
detection, forecasting, and is a generalization of the well-known Bayesian 
change-point problem.

We present an algorithm that computes the optimal expected reaction times for 
all $\alpha \in [0,1]$ such that $P(S>k)\leq \alpha$, and constructs the 
associated optimal stopping times $T$. Under certain conditions on 
$\{(X_i,Y_i)\}_{i\geq 1}$ and $S$ the algorithm running time is polynomial in 
$k$, and we illustrate this condition with two examples: a Bayesian change-point problem and a pure
tracking stopping time problem.