Optimisation techniques, based on the block model, for solving the optimum pit limit problem were discussed in an earlier paper. Of the available techniques the one based on graph theory proved to be the most attractive. In the graph theory model the vertices represent blocks and the arcs represent the mining restrictions. For large ore-bodies direct application of the graph theory method poses considerable computational and storage problems. Techniques for easing the computational effort by reducingthe problem size were introduced in an earlier paper. Further, significant computational savings can be made by exploiting the structure of the graph. This is done by building the graph up level by level and successively applying the graph theory algorithm to reduce the number of blocks. In building up the graph in this way one needs what is called a "search pattern" to indicate which arcs are to be added as new vertices are introduced. Moreover, as it is essential to keep the number of arcs to a minimum it is necessary to establish a "minimum search pattern".The problem of determining minimum search patterns for any block model and for any wall slope restrictions has not been considered in the literature.The objective of this paper is to present a complete solution to this problem and to discuss, through typical case studies, the application of the associated software developed.