In this article we summarize some aperiodic checkpoint placement algorithms for a software system over infinite and finite operation time horizons, and compare them in terms of computational accuracy. The underlying problem is formulated as the maximization of steady-state system availability and is to determine the optimal aperiodic checkpoint sequence. We present two exact computation algorithms in both forward and backward manners and two approximate ones; constant hazard approximation and fluid approximation, toward this end. In numerical examples with Weibull system failure time distribution, it is shown that the combined algorithm with the fluid approximation can calculate effectively the exact solutions on the optimal aperiodic checkpoint sequence.