We present the Skip lift, a randomized dictionary data structure inspired by the skip list [Pugh90, Comm. of the ACM]. Similar to the skip list, the skip lift has the finger search property: given a pointer to an arbitrary element f, searching for an element x takes expected O(logδ) time where δ is the rank distance between the elements x and f. The skip lift uses nodes of O(1) worst-case size (for a total of O(n) worst-case space usage) and it is one of the few efficient dictionary data structures that performs an O(1) worst-case number of structural changes (pointers/fields modifications) during an update operation. Given a pointer to the element to be removed from the skip lift the deletion operation takes O(1) worst-case time. © 2011 Elsevier B.V.
Bose, P., Douïeb, K., & Morin, P. (2012). Skip lift: A probabilistic alternative to red-black trees. In Journal of Discrete Algorithms (Vol. 14, pp. 13–20). https://doi.org/10.1016/j.jda.2011.12.017