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E#cient Tree Layout in a Multilevel Memory Hierarchy # Stephen Alstrup + Michael A. Bender # Erik D. Demaine

Summary: E#cient Tree Layout in a Multilevel Memory Hierarchy #
Stephen Alstrup + Michael A. Bender # Erik D. Demaine §
Martin Farach­Colton ¶ Theis Rauhe + Mikkel Thorup #
December 9, 2003
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 root­to­leaf 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 block­transfer 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
cache­oblivious setting in which the block­transfer size is unknown to the algorithm.
The query performance of the cache­oblivious layout is within a constant factor of
the query performance of the optimal known­block­size layout. Computing the cache­
oblivious layout requires only logarithmically many calls to the layout algorithm for
known block size; in particular, the cache­oblivious layout can be computed in O(N lg N)
time, where N is the number of nodes.


Source: Avrunin, George S. - Department of Mathematics and Statistics, University of Massachusetts at Amherst
Demaine, Erik - Computer Science and Artificial Intelligence Laboratory & Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (MIT)


Collections: Computer Technologies and Information Sciences; Mathematics