Divide-and-conquer algorithm: Difference between revisions

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=== Memory access ===
Divide-and-conquer algorithms naturally tend to make efficient use of [[memory cache]]s. The reason is that once a sub-problem is small enough, it and all its sub-problems can, in principle, be solved within the cache, without accessing the slower main memory. An algorithm designed to exploit the cache in this way is called ''[[cache-oblivious algorithm|cache-oblivious]]'', because it does not contain the cache size as an explicit parameter.<ref name="cahob">{{cite journal | author = M. Frigo |author2=C. E. Leiserson |author3=H. Prokop | title = Cache-oblivious algorithms | journal = Proc. 40th Symp. On the Foundations of Computer Science |pages=285–297 | year = 1999|url=https://dspace.mit.edu/bitstream/handle/1721.1/80568/43558192-MIT.pdf;sequence=2|doi=10.1109/SFFCS.1999.814600 |isbn=0-7695-0409-4 |s2cid=62758836 }}</ref> Moreover, D&C algorithms can be designed for important algorithms (e.g., sorting, FFTs, and matrix multiplication) to be ''optimal'' cache-oblivious algorithms–they use the cache in a probably optimal way, in an asymptotic sense, regardless of the cache size. In contrast, the traditional approach to exploiting the cache is ''blocking'', as in [[loop nest optimization]], where the problem is explicitly divided into chunks of the appropriate size—this can also use the cache optimally, but only when the algorithm is tuned for the specific cache sizes of a particular machine.
 
The same advantage exists with regards to other hierarchical storage systems, such as [[Non-uniform memory access|NUMA]] or [[virtual memory]], as well as for multiple levels of cache: once a sub-problem is small enough, it can be solved within a given level of the hierarchy, without accessing the higher (slower) levels.