Three major extensions to Kirkpatrick´s point location algorithm

Presents three extensions to D.G. Kirkpatrick´s (1983) point location algorithm. The extensions revolve around major focuses in the point location problem, namely the location of close successive query points and the dynamic and persistent implementations. The solutions described in this paper include (a) an algorithm that requires O(1) query time for reasonably close successive query points, with O(N) space bound and O(N) time to construct the search structure; (b) a dynamic implementation that require O(N) space, O(log N) query time and O(log N) update time; and (c) a persistent implementation of the same complexity as the dynamic interpretation. Two methods for modifying the search structure (the 𝒦-structure) dynamically and persistently are also discussed. The space requirements and query times of the dynamic and persistent methods are identical to their static counterparts. To affirm the practicality, conceptual simplicity and efficiency of the new methods, we implemented all these extensions, performed computational tests and compared them with other alternative schemes. The results reflect the expected efficiencies of the underlying design