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

**^**Harald Prokop. Cache-Oblivious Algorithms. Masters thesis, MIT. 1999.**^***Kumar, Piyush. “Cache-Oblivious Algorithms”. Algorithms for Memory Hierarchies. LNCS 2625. Springer Verlag: 193–212. CiteSeerX 10.1.1.150.5426.*- ^ Jump up to:
^{a}^{b}*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.* **^**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.- ^ Jump up to:
^{a}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.^{b}

Ofer Abarbanel – Executive Profile

Ofer Abarbanel is a 25 year securities lending broker and expert who has advised many Israeli regulators, among them the Israel Tax Authority, with respect to stock loans, repurchase agreements and credit derivatives. Founder of TBIL.co STATX Fund.