search at skip list at o(logk)

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I need to write a code that finds element x in a skip list. I need to implement that in O(logk) expected running time, where k is the location of x at the list (i.e., there are k-1 elements before x in the list).

I know how to do it at o(logn), but not o(logk).

can you show me the way? I need only general description or pseudo code, not more than that.

Posted 16-May-15 14:15pm

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Vadim Stadnik · Answer 1 · 2015-05-16T15:35:00

You can use finger search algorithm. It has the required running time, since it starts and ends at two nodes at the deepest level of a skip list. A variant of this algorithm is described and available in the article Efficient Representation of a Semigroup in C++[^], see Figure 1 for its illustration.

In general, note that level-linked B+ trees are better choice than skip lists, since they are deterministic data structures. In addition to this, I suggest measuring performance of both algorithms (top-down and finger search), if you are planning to use them in practical applications.

Regards,
Vadim Stadnik