In computing, a cache-oblivious algorithm (or cache-transcendent algorithm) is an algorithm designed to take advantage of a processor 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 loop tiling, 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. As 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 the 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.^{[citation needed]} In tuning for a specific machine, one may use a hybrid algorithm which uses loop tiling tuned for the specific cache sizes at the bottom level but otherwise uses the cache-oblivious algorithm.

The idea (and name) for cache-oblivious algorithms was conceived by Charles E. Leiserson as early as 1996 and first published by Harald Prokop in his master's thesis at the Massachusetts Institute of Technology in 1999. There were many predecessors, typically analyzing specific problems; these are discussed in detail in Frigo et al. 1999. Early examples cited include Singleton 1969 for a recursive Fast Fourier Transform, similar ideas in Aggarwal et al. 1987, Frigo 1996 for matrix multiplication and LU decomposition, and Todd Veldhuizen 1996 for matrix algorithms in the Blitz++ library.

In general, a program can be made more cache-conscious:

Cache-oblivious algorithms are typically analyzed using an idealized model of the cache, sometimes called the cache-oblivious model. This model is much easier to analyze than a real cache's characteristics (which have complex associativity, replacement policies, etc.), but in many cases is provably within a constant factor of a more realistic cache's performance. It is different than the external memory model because cache-oblivious algorithms do not know the block size or the cache size.

In particular, the cache-oblivious model is an abstract machine (i.e., a theoretical model of computation). It is similar to the RAM machine model which replaces the Turing machine's infinite tape with an infinite array. Each location within the array can be accessed in ${\displaystyle O(1)}$ time, similar to the random-access memory on a real computer. Unlike the RAM machine model, it also introduces a cache: the second level of storage between the RAM and the CPU. The other differences between the two models are listed below. In the cache-oblivious model:

To measure the complexity of an algorithm that executes within the cache-oblivious model, we measure the number of cache misses that the algorithm experiences. Because the model captures the fact that accessing elements in the cache is much faster than accessing things in main memory, the running time of the algorithm is defined only by the number of memory transfers between the cache and main memory. This is similar to the external memory model, which all of the features above, but cache-oblivious algorithms are independent of cache parameters (${\displaystyle B}$ and ${\displaystyle M}$). The benefit of such an algorithm is that what is efficient on a cache-oblivious machine is likely to be efficient across many real machines without fine-tuning for particular real machine parameters. For many problems, an optimal cache-oblivious algorithm will also be optimal for a machine with more than two memory hierarchy levels.