An optimal algorithm for extracting the regions of a plane graph

Abstract In a recent paper, Fan and Chang (1991) presented an algorithm for extracting all regions of a plane graph. It is shown in this paper that their algorithm has quadratic time and space complexity. We propose an optimal algorithm which takes O(m log m) computation time and uses O(m) space, where m is the number of edges of the plane graph. The optimality of our algorithm is established by proving an Ω(m log m) lower bound under the algebraic decision-tree model.