Cache-oblivious algorithm

In computing, a cache-oblivious algorithm (or cache-transcendent algorithm) is an algorithm designed to take advantage of a CPU cache without having the size of the cache (or the length of the cache lines, etc.) as an explicit parameter.

An optimal cache-oblivious algorithm is a cache-oblivious algorithm that uses the cache optimally (in an asymptotic sense, ignoring constant factors). Thus, a cache-oblivious algorithm is designed to perform well, without modification, on multiple machines with different cache sizes, or for a memory hierarchy with different levels of cache having different sizes. Cache-oblivious algorithms are contrasted with explicit blocking, as in loop nest optimization, which explicitly breaks a problem into blocks that are optimally sized for a given cache.

Optimal cache-oblivious algorithms are known for matrix multiplication, matrix transposition, sorting, and several other problems. Some more general algorithms, such as Cooley–Tukey FFT, are optimally cache-oblivious under certain choices of parameters. Because these algorithms are only optimal in an asymptotic sense (ignoring constant factors), further machine-specific tuning may be required to obtain nearly optimal performance in an absolute sense. The goal of cache-oblivious algorithms is to reduce the amount of such tuning that is required.

Typically, a cache-oblivious algorithm works by a recursive divide and conquer algorithm, where the problem is divided into smaller and smaller subproblems. Eventually, one reaches a subproblem size that fits into cache, regardless of the cache size. For example, an optimal cache-oblivious matrix multiplication is obtained by recursively dividing each matrix into four sub-matrices to be multiplied, multiplying the submatrices in a depth-first fashion. In tuning for a specific machine, one may use a hybrid algorithm which uses blocking tuned for the specific cache sizes at the bottom level, but otherwise uses the cache-oblivious algorithm.

References

  1. ^Harald Prokop. Cache-Oblivious Algorithms. Masters thesis, MIT. 1999.
  2. ^Kumar, Piyush. “Cache-Oblivious Algorithms”. Algorithms for Memory Hierarchies. LNCS 2625. Springer Verlag: 193–212. CiteSeerX 10.1.1.150.5426.
  3. ^ Jump up to:ab Frigo, M.; Leiserson, C. E.; Prokop, H.; Ramachandran, S. (1999). Cache-oblivious algorithms (PDF). Proc. IEEE Symp. on Foundations of Computer Science (FOCS). pp. 285–297.
  4. ^Daniel Sleator, Robert Tarjan. Amortized Efficiency of List Update and Paging Rules. In Communications of the ACM, Volume 28, Number 2, p.202-208. Feb 1985.
  5. ^ Jump up to:ab Erik Demaine. Cache-Oblivious Algorithms and Data Structures, in Lecture Notes from the EEF Summer School on Massive Data Sets, BRICS, University of Aarhus, Denmark, June 27–July 1, 2002.

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