Many problems of practical interest involve line-of-sight on a topographic surface. Some such problems can be successfully studied on the basis of the mutual visibility among a finite number of representative points. Such visibility problems can be formalized and resolved as graph problems. In this paper, we show that graph algorithms can be useful to find efficient solutions for discrete visibility problems in several cases. On the basis of results from the theory of complexity, we give some practical rules to apply such an approach. We further investigate the solution of some relevant visibility problems under this perspective.