A systolic algorithm for extracting regions from a planar graph

Let us consider Fig. 1. In Fig. 1, there are four regions, as indicated (R4 9 epresents the entire space not occupied by the graph). Suppose we are given all of he edges of the graph and their geometrical orientation. Can we find all of the 'egions automatically? A similar problem was discussed in [Nie 82]. In their )roblem, we are given a polygon which is not simple and we are asked to produce dl regions formed by the intersecting line segments of the polygon. In this paper, we shall show that indeed we can. We have designed a systolic dgorithm to produce all of these regions. This paper is organized as follows: Some definitions and notations are given in ;ection 2. An overall picture of our algorithm is given in Section 3. Sections 4 and 5 ntroduce the systolic algorithm. Concluding remarks and future research are )resented in Section 6.