Cache-Oblivious Searching and Sorting

M.Sc. Thesis by Frederik Rønn


Algorithms that use multi-layered memory hierarchies efficiently have traditionally relied on detailed knowledge of the characteristics of memory systems. The cache-oblivious approach changed this in 1999 by making it possible to design memory-efficient algorithms for hierarchical memory systems without such detailed knowledge. As a consequence, one single implementation of a cache-oblivious algorithm is efficient on any memory hierarchy. The purpose of the thesis is to investigate the behavior of cache-oblivious searching and sorting algorithms through constant-factors analysis and benchmarking.

Cache-oblivious algorithms are analyzed in the ideal-cache model, which is an abstraction of real memory systems. We investigate the assumptions of the model in order to determine the accuracy of cache-complexity bounds derived by use of the model.

We derive the constant factors of the cache complexities of cache-oblivious, cache-aware, and traditional searching and sorting algorithms in the ideal-cache model. The constant factors of the work complexities of the algorithms are derived in the pure-C cost model. The analyses are verified through benchmarking of implementations of all algorithms.

For the searching algorithms, our constant-factors analysis predicts the benchmark results quite precisely --- considering both memory performance and work complexity. For the more complex sorting algorithms our results show the same pattern, though the similarities between predicted and measured performance are not as significant.

Furthermore, we develop a new algorithm that lays out a cache-oblivious static search tree in memory in linear time, which is an improvement of the algorithms known so far.

We conclude that by combining the ideal-cache model and the pure-C model, the relative performance of programs can be predicted quite precisely, provided that the analysis is carefully done.

The following files are available for download: