Space-Efficient Functional Offline-Partially-Persistent Trees with Applications to Planar Point Location.

In 1989 Driscoll, Sarnak, Sleator, and Tarjan presented general space-efficient transformations for making ephemeral data structures persistent. The main contribution of this paper is to adapt this transformation to the functional model. We present a general transformation of an ephemeral, linked data structure into an offline, partially persistent, purely functional data structure with additive $$\mathcal {O}\!\left( n\log n \right) $$ construction time and $$\mathcal {O}\!\left( n \right) $$ space overhead; with n denoting the number of ephemeral updates. An application of our transformation allows the elegant slab-based algorithm for planar point location by Sarnak and Tarjan 1986 to be implemented space efficiently in the functional model using linear space.