Skip Lift: A Probabilistic Alternative to Red-Black Trees

We present the Skip lifts, a randomized dictionary data structure inspired from the skip list [Pugh ’90, Comm. of the ACM]. Similarly to the skip list, the skip lifts has the finger search property: Given a pointer to an arbitrary element f , searching for an element x takes expected O(log δ) time where δ is the rank distance between the elements x and f . The skip lifts uses nodes of O(1) worst-case size and it is one of the few efficient dictionary data structures that performs an O(1) worstcase number of structural changes during an update operation. Given a pointer to the element to be removed from the skip lifts the deletion operation takes O(1) worst-case time.