A bucketing algorithm for the orthogonal segment intersection search problem and its practical efficiency

The orthogonal segment intersection search problem is stated as follows: given a set S of n orthogonal segments in the plane, report all the segments of S that intersect a given orthogonal query segment. For this problem, we propose a simple and practical algorithm based on bucketing techniques. It constructs, in O(n) time preprocessing, a search structure of size O(n) so that all the segments of S intersecting a query segment can be reported in O(k) time in the average case, where k is the number of the reported segments. The proposed algorithm as well as existing algorithms is implemented in FORTRAN, and their practical efficiencies are investigated through computational experiments. It is shown that our O(k) search time, O(n) space, and O(n) preprocessing time algorithm is in practice the most efficient among the algorithms tested.