Sorting jordan sequences in linear time using level-linked search trees

For a Jordan curve C in the plane nowhere tangent to the x axis, let x₁, x₂,..., x_n be the abscissas of the intersection points of C with the x axis, listed in the order the points occur on C. We call x₁, x₂,..., x_n a Jordan sequence. In this paper we describe an O(n)-time algorithm for recognizing and sorting Jordan sequences. The problem of sorting such sequences arises in computational geometry and computational geography. Our algorithm is based on a reduction of the recognition and sorting problem to a list-splitting problem. To solve the list-splitting problem we use level-linked search trees.