Qualitative Spatial and Temporal Reasoning (QSTR) represents spatial and temporal information in terms of human comprehensible qualitative predicates and reasons about qualitative information by solving qualitative constraint networks (QCNs). Despite significant progress in the past three decades, more and more evidence has shown that it is inherently hard to find exact solutions for expressive qualitative constraints. In many applications, however, we are often required to make decisions in a very limited time. In these cases, finding a good approximate solution in seconds is much more desirable than waiting days for an exact solution. In this paper, we will exploit the algebraic structure of qualitative calculi (e.g. Interval Algebra and RCC8) as well as their conceptual neighbourhood graphs to develop approximate methods for consistency checking in QSTR. Moreover, we propose and empirically compare four independent methods to serve as tools for finding good approximate solutions for the given qualitative calculi.