2002/11/12 by Stephen Alstrup, Michael A. Bender, Alstrup, Stephen +10
Computer Science · #Algorithms and Data Compression #Data Structures and Algorithms (cs.DS) #E.1 #F.2.2 #FOS: Computer and information sciences #Graph Theory and Algorithms #Parallel Computing and Optimization Techniques #cs.DS
paper · pdf · doi:10.48550/arxiv.cs/0211010
18 pages. Version 2 adds faster dynamic programs. Preliminary version appeared in European Symposium on Algorithms, 2002
openalex publication_date 2002/11/12 · arxiv created 2004/07/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.