The Influence of Caches on the Performance of Sorting

Abstract

We i n vestigate the e ect that caches have on the performance of sorting algorithms both experimentally and analytically. To address the performance problems that high cache miss penalties introduce we restructure mergesort, quicksort, and heapsort in order to improve their cache locality. F or all three algorithms the improvement i n c a c he performance leads to a reduction in total execution time. We also investigate the performance of radix sort. Despite the extremely low instruction count incurred by this linear time sorting algorithm, its relatively poor cache performance results in worse overall performance than the e cient comparison based sorting algorithms. For each algorithm we provide an analysis that closely predicts the number of cache misses incurred by the algorithm.

A UNIQUE SORTING ALGORITHM WITH LINEAR TIME & SPACE COMPLEXITY

“…Complexities of algorithms are strictly dependent on input size, caches performance etc., briefly description about complexities of algorithms are given some of the noble work [28] [29] [30].…”

A dynamically tuned sorting library

“…A drawback is that multi-quicksort cannot be done efficiently in-place and executes more instructions that the base quicksort. The results in [7] show that the execution times of multi-quicksort and our implementation of quicksort, which is based on Sedgewick's proposed optimizations, are very close even for large data sets. Thus, we did not implement multi-quicksort.…”

“…A large number of sorting algorithms have been proposed and their asymptotic complexity, in terms of the number of comparisons or number of iterations, has been carefully analyzed [6]. In the recent past, there has been a growing interest on improvements to sorting algorithms that do not affect their asymptotic complexity but nevertheless improve performance by enhancing data locality [4,7,8]. The algorithms resulting from these improvements have been called cache-conscious.…”

“…Quicksort. Lamarca et al [7] evaluate a memory-optimized version of quicksort that they call multi-quicksort. When the number of keys to sort is larger than the cache size, multi-quicksort uses several pivots to divide the set of keys into subsets which are likely to fit in the cache.…”

“…This optimization eliminates the overhead of calling the insertion sort procedure during the recursion, and as a result, it reduces the number of executed instructions. However, sorting these small partitions as they appear during the recursion procedure, reduces the number of cache misses because the elements to be sorted are already in the cache [7]. Since it is not clear which of these two strategies results in a lower execution time, we try both optimizations when installing our library and choose the one that results in best performance.…”