A skip list is a probabilistic data structure designed to facilitate efficient search, insertion, and deletion operations.

At its core, a skip list is a linked list enhanced with additional forward pointers at various levels, which enable faster traversal of the data. The term “skip list” originates from these forward pointers, which allow us to bypass multiple nodes when searching for a specific element, thus accelerating the search process.

The structure of a skip list comprises multiple sorted linked lists, where each list represents a subset of the list that is directly below it. The bottom-level list contains all the elements, while each successive higher-level list includes a randomly selected subset of the elements from the level beneath. The top-level list contains the fewest elements, and the number of elements decreases as we ascend through the levels. This hierarchical structure allows for efficient search operations; we begin at the top level and move downward until we locate the desired element.

The efficiency of a skip list arises from its ability to combine the advantages of a sorted array, which offers quick search times, with those of a linked list, which allows for rapid insertion and deletion operations. The forward pointers permit us to bypass extensive sections of the list during searches, akin to how one might quickly locate an element in a sorted array by jumping to the middle and eliminating half the possibilities. Additionally, because a skip list retains its fundamental nature as a linked list, we can swiftly insert or remove elements by adjusting a few pointers, without the need to shift large portions of data.

In terms of time complexity, the average and worst-case complexities for search, insertion, and deletion operations in a skip list are both $O(\log n)$, where $n$ represents the number of elements in the list. This efficiency makes skip lists a compelling choice for various applications. However, it is important to note that they do require more memory than a standard linked list due to the additional forward pointers.