Paper by Erik D. Demaine

Reference:

Stephen Alstrup, Michael A. Bender, Erik D. Demaine, Martin Farach-Colton, J. Ian Munro, Theis Rauhe, and Mikkel Thorup, “Efficient Tree Layout in a Multilevel Memory Hierarchy”, Manuscript, December 2003.

Abstract:

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 Ω(lg B / lg lg B) and O(lg B) when compared to the optimal layout.

Comments:

This paper is also available as arXiv:cs.DS/0211010 of the Computing Research Repository (CoRR).

This paper replaces and rectifies the ESA version.

Length:

The paper is 14 pages.

Availability:

The paper is available in PostScript (367k), gzipped PostScript (165k), and PDF (201k).

See information on file formats.

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Related papers:

TreeLayout_ESA2002 (Efficient Tree Layout in a Multilevel Memory Hierarchy)