Treap with implicit keys

Question

There\'s a data structure called treap: that\'s a randomized binary search tree, which is also a heap on randomly generated so-called \"priorities\".

There\'s a vari

Answer 1

Maybe you are looking for a Rope (complex form of string) modified to your needs for delayed operations. Interesting thing is that there is an open question regarding ropes right here right now.

Answer 2

I don't think there is a name for that data structure since it is simply a combination of two orthogonal concepts. You could use implicit keys like this with just about any self-balancing tree data structure.

You might want to take a look at Scapegoat trees, since they use the subtree size already for rebalancing and do not require any per-node overhead.

Answer 3

You can find this data structure in the paper by Kaplan and Verbin on sorting signed permutations by reversals (page 7, section 3.1): http://www.math.jussieu.fr/~fouquet/ENSEIGNEMENT/PROJETS/kaplan.pdf.

Answer 4

The key idea (no pun intended!) in treaps is to use keys, which are randomized. If you remove the keys, I don't see how you can have a treap: so perhaps I misunderstood your question. Or perhaps you are referring to the alternative to treaps, the randomized binary search tree. Both data structures use the same idea that you can attain average-case complexity by making sure your tree looks like an average tree (instead of a pathological case).

With the treaps, you do this using random priorities and balancing.

With randomized binary trees, the randomness is solely included during the construction: that is, when you insert a node in tree T, it has probability 1/(size(T) + 1) to be at the root, where size(T) is the number of nodes of T; and of course if the node is not inserted at the root, you continue recursively until it is added. (See articles my C. Martinez for a detailed study of these trees.)

This data structure behaves exactly like a treap, but uses a different mechanism that does not require keys.

If this is not what you were looking for, perhaps you could share some additional information: did your lecturer mention anybody who might have worked on this structure, where did you here this lecturer and what his/your nationality. It might not seem like it, but knowing your native tongue could be an important clue as you can generally peg down algorithms/data structures to a specific country that originated it.