Today I read a paper titled “Efficient Tree Layout in a Multilevel Memory Hierarchy”
The abstract is:
We consider the problem of laying out a tree with fixed parent/child structure in hierarchical memory.
The goal is to minimize the expected number of block transfers performed during a search along a root-to-leaf path, subject to a given probability distribution on the leaves.
This problem was previously considered by Gil and Itai, who developed optimal but slow algorithms when the block-transfer size B is known.
We present faster but approximate algorithms for the same problem; the fastest such algorithm runs in linear time and produces a solution that is within an additive constant of optimal.
In addition, we show how to extend any approximately optimal algorithm to the cache-oblivious setting in which the block-transfer size is unknown to the algorithm.
The query performance of the cache-oblivious layout is within a constant factor of the query performance of the optimal known-block-size layout.
Computing the cache-oblivious layout requires only logarithmically many calls to the layout algorithm for known block size; in particular, the cache-oblivious layout can be computed in O(N lg N) time, where N is the number of nodes.
Finally, we analyze two greedy strategies, and show that they have a performance ratio between Omega(lg B / lg lg B) and O(lg B) when compared to the optimal layout.